This blog is a platform of Physics/maths/science for Engineering and Medical entrance examination like IITJEE,AIEEE,CBSE board exams.
CSIRNET and GATE physics: de Brogli wavelength
CSIRNET and GATE physics: de Brogli wavelength: "Interference, diffraction and polarization establishes the wave nature of light and can be explained on the basis of wave theory photoelectr..."
Sample questions for AISSCE board exams
Try to solve these questions on your own in my net post I'll publish 3 marks and 5 marks sample questions.
Question 1. W cm apart on a hat is the amount of work done in moving 100 nC charge between two points 5 cm apart on an equipotential surface? 1
Question 2. What is the value of refractive index of medium of polarising angle 60 degree? 1
Question 3. State two factors on which temperature of inversion of a thermocouple may depend. 1
Question 4. In which direction would a compass needle align if taken to geographic (i) north and (ii) south pole? 1
Question 5. The instantaneous voltage from an a.c. source is given by E=300 sin 314t . What is the r.m.s. voltage of the source? 1
Question 6. Compare the radii of two nuclei with mass number 1 and 27 respectively. 1
Question 7. How does energy gap in an intrinsic semiconductor vary, when doped with a pentavalent impurity. 1
Question 8. If the temperature of good conductor increases, how does the relaxation time of electrons in the conductor change. 1
Question 9. Draw a labelled ray digram shwing the formation of image using a Newtonian type reflecting telescope. 2
Question 10. The output voltage of an ideal transformer, connected to a 240 V a.c. is 24 V. When transformer is used to light a bulb with rating 24 V , 24 W, calculate the current in the primary coil of the circuit. 2
Question 11. Can magnetic field set a resting electron into motion. 2
Question 12. You are given two niclei _{3}X7 and _{3}Y4. Are they isotopes of same element? State the resion . Which one of the two nuclei is likely to be more stable. 2
Question 13. A heater coil is rated 100 W , 200 V. It is cut into two identical parts. Both parts are connected togather in parallel , to the same source of 200 V. Calculate the energy librated per second in new combination. 2
Question 14. A charge q moving in a straight line is accelerated by potential difference V. It enters uniform magnetic field B perpandicular to its path . Deduce in terms of V an expression for the radius of circular path in which it travels. 2
Question 15. State the reason for the following observations recorded from the surface of the moon:
(i) sky appears dark
(ii) rainbow is never formed.
Question 16. Write any three characterstics , a ferromagnetic substance should posess , if it is to be used to make a permanent magnet. Give one example of such material. 2
Question 17. The value of ground state of hydrogen atom is 13.6 eV.
(i) What does the negative sign signify.
(ii) how much energy is required to take an electron in this atom from ground state to the first exited state. 2
Question 1. W cm apart on a hat is the amount of work done in moving 100 nC charge between two points 5 cm apart on an equipotential surface? 1
Question 2. What is the value of refractive index of medium of polarising angle 60 degree? 1
Question 3. State two factors on which temperature of inversion of a thermocouple may depend. 1
Question 4. In which direction would a compass needle align if taken to geographic (i) north and (ii) south pole? 1
Question 5. The instantaneous voltage from an a.c. source is given by E=300 sin 314t . What is the r.m.s. voltage of the source? 1
Question 6. Compare the radii of two nuclei with mass number 1 and 27 respectively. 1
Question 7. How does energy gap in an intrinsic semiconductor vary, when doped with a pentavalent impurity. 1
Question 8. If the temperature of good conductor increases, how does the relaxation time of electrons in the conductor change. 1
Question 9. Draw a labelled ray digram shwing the formation of image using a Newtonian type reflecting telescope. 2
Question 10. The output voltage of an ideal transformer, connected to a 240 V a.c. is 24 V. When transformer is used to light a bulb with rating 24 V , 24 W, calculate the current in the primary coil of the circuit. 2
Question 11. Can magnetic field set a resting electron into motion. 2
Question 12. You are given two niclei _{3}X7 and _{3}Y4. Are they isotopes of same element? State the resion . Which one of the two nuclei is likely to be more stable. 2
Question 13. A heater coil is rated 100 W , 200 V. It is cut into two identical parts. Both parts are connected togather in parallel , to the same source of 200 V. Calculate the energy librated per second in new combination. 2
Question 14. A charge q moving in a straight line is accelerated by potential difference V. It enters uniform magnetic field B perpandicular to its path . Deduce in terms of V an expression for the radius of circular path in which it travels. 2
Question 15. State the reason for the following observations recorded from the surface of the moon:
(i) sky appears dark
(ii) rainbow is never formed.
Question 16. Write any three characterstics , a ferromagnetic substance should posess , if it is to be used to make a permanent magnet. Give one example of such material. 2
Question 17. The value of ground state of hydrogen atom is 13.6 eV.
(i) What does the negative sign signify.
(ii) how much energy is required to take an electron in this atom from ground state to the first exited state. 2
CSIRNET and GATE physics: One Dimensional Oscillator (small oscillations)
CSIRNET and GATE physics: One Dimensional Oscillator (small oscillations): "Consider a system with one degree of freedom and one generalized coordinate q. For small displacement from the equilibrium we can expand po..."
Questions and answers for AISSCE board exams
Question 1. Why electron capture is common in case of heavy nucleus?
Answer. A heavy nucleus has large positive charge. Moreover, the raidus of Kshell in heavy nuclei is much smaller than that in case of light nucleus. Due to both these factors, the Kshell electrons experiences a large force of attraction due to positive nucleus and is keptured by it.
Question 2. Why is nuclear fusion difficult to carry out?
Answer. The fusion reaction require very high temperature condition and it has to be obtained by causing explosion due to fission process. Further , due to very high temperature no material can sustain the region where fusion is to be carried out.
Question 3. Would you prefer to use a transistor in CB or CE as a amplifier?
Answer. Transistor in CE configuration as an amplifier as curent gain in this case is more than that as in case of amplifier in CB configuration.
Question 4. Explain why the core of the transformer is laminated?
Answer. The core of a transformer is laminated so as to reduce loss of energy due to eddy currents. The magnitude of the eddy currents set up is considerably minimised, when the core is laminated.
Question 5. Why is the core of a transformer made of a magnetic material of high permeability?
Answer. The transformer works on the principle of mutual induction. In case, the core has a high value of magnetic permeability, the magnetic field lines will crowd through the core and the magnetic flux linkage between the two coils will also be large.
Question 6. When the motor of an electric refrigerator starts, the lights in the house become dim momentarily. Why?
Answer. When the electric motor of the refrigerator starts, it draws maximum current from the a.c. mains. It is because, just at the start of the motor, the back e.m.f. is zero. Due to the large current drawn by the motor, the current through the lights (connected in parallel) decreases and they become dim. However, as the armature of the motor rotates, back e.m.f. is produced and the motor draws current less than that drawn in the beginning . Then, the lights recover their brilliance.
Answer. A heavy nucleus has large positive charge. Moreover, the raidus of Kshell in heavy nuclei is much smaller than that in case of light nucleus. Due to both these factors, the Kshell electrons experiences a large force of attraction due to positive nucleus and is keptured by it.
Question 2. Why is nuclear fusion difficult to carry out?
Answer. The fusion reaction require very high temperature condition and it has to be obtained by causing explosion due to fission process. Further , due to very high temperature no material can sustain the region where fusion is to be carried out.
Question 3. Would you prefer to use a transistor in CB or CE as a amplifier?
Answer. Transistor in CE configuration as an amplifier as curent gain in this case is more than that as in case of amplifier in CB configuration.
Question 4. Explain why the core of the transformer is laminated?
Answer. The core of a transformer is laminated so as to reduce loss of energy due to eddy currents. The magnitude of the eddy currents set up is considerably minimised, when the core is laminated.
Question 5. Why is the core of a transformer made of a magnetic material of high permeability?
Answer. The transformer works on the principle of mutual induction. In case, the core has a high value of magnetic permeability, the magnetic field lines will crowd through the core and the magnetic flux linkage between the two coils will also be large.
Question 6. When the motor of an electric refrigerator starts, the lights in the house become dim momentarily. Why?
Answer. When the electric motor of the refrigerator starts, it draws maximum current from the a.c. mains. It is because, just at the start of the motor, the back e.m.f. is zero. Due to the large current drawn by the motor, the current through the lights (connected in parallel) decreases and they become dim. However, as the armature of the motor rotates, back e.m.f. is produced and the motor draws current less than that drawn in the beginning . Then, the lights recover their brilliance.
CSIRNET and GATE physics: Stable and unstable equilibrium
CSIRNET and GATE physics: Stable and unstable equilibrium: "First consider the figures given below Above are the plots of potential energy as a function of x , for a particle executing bound..."
Manage yourself for competetions (think about these thoughts)
1. First of all have a positive attitude it pays and whatever you are thinking of doing do it now i mean start doing whatever you are planning to do or have planned to do so far.
2. Try and manage your stress levels , if stressed most easy part of your syllabus would seem hard and difficult to learn. So maintain your cool.
3. Do not panic if you failed once think about your mistakes, identify your weak link and start preparing again with only success in your mind. Remember that failure means delay not the defeat.
4. Never let yourself be stopped by the loss of one opportunity , think , discover another one and start working for it.
5. Organise yourself so that you can make best out of your limited time.
7. Last but not the least try being fair and genuine with your competitors.
2. Try and manage your stress levels , if stressed most easy part of your syllabus would seem hard and difficult to learn. So maintain your cool.
3. Do not panic if you failed once think about your mistakes, identify your weak link and start preparing again with only success in your mind. Remember that failure means delay not the defeat.
4. Never let yourself be stopped by the loss of one opportunity , think , discover another one and start working for it.
5. Organise yourself so that you can make best out of your limited time.
7. Last but not the least try being fair and genuine with your competitors.
Manage yourself for competetions (think about these thoughts)
1. First of all have a positive attitude it pays and whatever you are thinking of doing do it now i mean start doing whatever you are planning to do or have planned to do so far.
2. Try and manage your stress levels , if stressed most easy part of your syllabus would seem hard and difficult to learn. So maintain your cool.
3. Do not panic if you failed once think about your mistakes, identify your weak link and start preparing again with only success in your mind. Remember that failure means delay not the defeat.
4. Never let yourself be stopped by the loss of one opportunity , think , discover another one and start working for it.
5. Organise yourself so that you can make best out of your limited time.
7. Last but not the least try being fair and genuine with your competitors.
2. Try and manage your stress levels , if stressed most easy part of your syllabus would seem hard and difficult to learn. So maintain your cool.
3. Do not panic if you failed once think about your mistakes, identify your weak link and start preparing again with only success in your mind. Remember that failure means delay not the defeat.
4. Never let yourself be stopped by the loss of one opportunity , think , discover another one and start working for it.
5. Organise yourself so that you can make best out of your limited time.
7. Last but not the least try being fair and genuine with your competitors.
IITJEE previous year questions
Question 1
A particle executes SHM with frequency f. The frequency with which its Kinetic energy oscillates is
(a) f/2
(b) f
(c) 2f
(d) 4f
Question 2
A linear harmonic oscillator of force constant 2 x 10^{6}N/m and amplitude 0.01 m has a total mechanical energy of 160J. Its
(a) Maximum potential energy is 100J
(b) Maximum kinetic energy is 100J
(c) Maximum potential energy is 160J
(d) Minimum potential energy is zero
Question 3
A given quantity of ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of gas is
(a) 2P/3
(b) P
(c) 3P/2
(d) 2P
Question 4
During the melting of slab of ice at 273K at atmospheric pressure
(a) positive work is done by the ice water system on the atmosphere
(b) positive work is done on the ice water system by the atmosphere
(c) the internal energy of the ice water system increases
(d) the internal energy of the ice water system decreases
Question 5
When an ideal diatomic gas is heated at a constant pressure , the fraction of the heat energy supplied which increases the internal energy of the gas is
(a) 2/5
(b) 3/5
(c) 3/7
(d) 5/7
Question 6
In a given process on an ideal gas , dW=0 and dQ<0. then for the gas
(a) the temperature will decrease
(b) the volume will increase
(c) the pressure will remain constant
(d) the temperature will increase
Question 7
A cylinder rolls up an inclined plane, reaches some hight, and then rolls down (without slipping through these motions). The directions of frictional force acting on the cylinder are
(a) up the incline while ascending and down the incline descending
(b) up the incline while ascending as well as descending
(c) down the incline while ascending and up the incline while descending
(d) down the incline while ascending as well as descending
Answer
1. c
2. c,d
3. b
4. b,c
5. d
6. a
7. b
A particle executes SHM with frequency f. The frequency with which its Kinetic energy oscillates is
(a) f/2
(b) f
(c) 2f
(d) 4f
Question 2
A linear harmonic oscillator of force constant 2 x 10^{6}N/m and amplitude 0.01 m has a total mechanical energy of 160J. Its
(a) Maximum potential energy is 100J
(b) Maximum kinetic energy is 100J
(c) Maximum potential energy is 160J
(d) Minimum potential energy is zero
Question 3
A given quantity of ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of gas is
(a) 2P/3
(b) P
(c) 3P/2
(d) 2P
Question 4
During the melting of slab of ice at 273K at atmospheric pressure
(a) positive work is done by the ice water system on the atmosphere
(b) positive work is done on the ice water system by the atmosphere
(c) the internal energy of the ice water system increases
(d) the internal energy of the ice water system decreases
Question 5
When an ideal diatomic gas is heated at a constant pressure , the fraction of the heat energy supplied which increases the internal energy of the gas is
(a) 2/5
(b) 3/5
(c) 3/7
(d) 5/7
Question 6
In a given process on an ideal gas , dW=0 and dQ<0. then for the gas
(a) the temperature will decrease
(b) the volume will increase
(c) the pressure will remain constant
(d) the temperature will increase
Question 7
A cylinder rolls up an inclined plane, reaches some hight, and then rolls down (without slipping through these motions). The directions of frictional force acting on the cylinder are
(a) up the incline while ascending and down the incline descending
(b) up the incline while ascending as well as descending
(c) down the incline while ascending and up the incline while descending
(d) down the incline while ascending as well as descending
Answer
1. c
2. c,d
3. b
4. b,c
5. d
6. a
7. b
Poisson's Ratio
σ =β/α
since,
longitudinal strain = α = Δl/l and
lateral strain = β = ΔD/D
hence poisson's ratio is σ =lΔD/DΔl
Tags: Elasticity
Hamiltonian Formulism of mechanics (part 1)
Hamiltonian is H=T+V
or,
Hamilton's Canonical Equations of motion:
or,
Hamilton's Canonical Equations of motion:
 Coordinates cyclic in Lagrangian will also be cyclic in Hamiltonian.
 Canonical transformations are characterized by the property that they leave the form of Hamilton's equations of motion invarient.
 Lagrange's equation of motion are covarient w.r.t. point transformations (Q_{j}=Q_{j}(q_{j},t) and if we define P_{j} as,
the Hamilton's canonical equation will also be covarient.
 Consider the transformationsQ_{j}=Q_{j}(p,q,t)P_{j}=P_{j}(p,q,t)where Q_{j} and P_{j} are new set of coordinates.
 For Q_{j} and P_{j} to be canonical they should be able to be expressed in Hamiltonian form of equations of motion i.e.,where, K=K(Q,P,t) and is substitute of Hamiltonian H of old set in new set of coordinates.
 Q_{j} and P_{j} to be canonical must also satisfy modified Hamilton's principle i.e.,
 Using same principle for old set q_{j} and p_{j}where F is any function of phase space coordinates with continous second derivative.
 Term ∂F/∂t in 1 contributes to the variation of the action integral only at end points and will therefore vanish if F is a function of (q,p,t) or (Q,P,t) or any mixture of phase space coordinates since they have zero variation at end points.
 F is useful for specifying the exact form of anonical transformations only when half of the variables (except time) are from the old set and half from the new set.
 F acts as bridge between two sets of canonical variables and is known as generating function of transformations.
Objective Type questions : Test Yourself
1. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
(a) x^{2}
(b) e^{x}
(c) x
(d) log_{e} x
2. Which of the following statements is false for a particle moving in a circle with a constant angular speed.
(a) The velocity vector is tangent to the circle
(b) the acceleration vector is tangent to the circle
(c) the acceleration vector points to the centre of the circle
(d) the velocity and acceleration vectors are perpandicular to each other
3. If A × B = B × A, then angle between both the vectors is
(a) π
(b) π/3
(c) π/2
(d) π/4
4. A ball is released from top of the tower of hight h m. It takes t sec. to reach the ground. What is the position of ball in T/3 sec.
(a) h/9 m from the ground
(b) 7h/9 m from the ground
(c) 8h/9 m from the ground
(d) 17h/18 m from the ground
5. A machine gun fires a bullet of mass 40g with a velocity 1200 m/s. the man holding it can exert a maximum force 144 N on the gun. How many bullets can he fire per second at the most.
(a) one
(b) four
(c) two
(d) three
Answer
1. a
2. b
3. a
4. c
5. d
(a) x^{2}
(b) e^{x}
(c) x
(d) log_{e} x
2. Which of the following statements is false for a particle moving in a circle with a constant angular speed.
(a) The velocity vector is tangent to the circle
(b) the acceleration vector is tangent to the circle
(c) the acceleration vector points to the centre of the circle
(d) the velocity and acceleration vectors are perpandicular to each other
3. If A × B = B × A, then angle between both the vectors is
(a) π
(b) π/3
(c) π/2
(d) π/4
4. A ball is released from top of the tower of hight h m. It takes t sec. to reach the ground. What is the position of ball in T/3 sec.
(a) h/9 m from the ground
(b) 7h/9 m from the ground
(c) 8h/9 m from the ground
(d) 17h/18 m from the ground
5. A machine gun fires a bullet of mass 40g with a velocity 1200 m/s. the man holding it can exert a maximum force 144 N on the gun. How many bullets can he fire per second at the most.
(a) one
(b) four
(c) two
(d) three
Answer
1. a
2. b
3. a
4. c
5. d
Constrains and constrained motion
 A constrained motion is a motion which can not proceed arbitrary in any manner.
 Particle motion can be restricted to occur (1) along some specified path (2) on surface (plane or curved) arbitrarily oriented in space.
 Imposing constraints on a mechanical system is done to simplify the mathematical description of the system.
 Constraints expressed in the form of equation f(x_{1},y_{1},z_{1},......,x_{n},y_{n},z_{n} :t)=0 are called holonomic constraints.
 Constraints not expressed in this fashion are called nonholonomic constraints.
 Scleronomic conatraints are independent of time.
 Constraints containing time explicitely are called rehonomic.
 Therefore a constraint is either
and either
"holonomic where constraints relations can be made independent of velocity or nonholonomic where these relations are irreducible functions of velocity"
Constraints types of some physicsl systems are given below in the table
How to simplify circuits with resistors
1. In any given circuit first of all recognize the resistances connected in series then by summing the individual resistances draw a new, simplified circuit diagram.
For series combination of resistances equivalent resistance is given by the equation
R_{eq}= R_{1} + R_{2}+R_{3}
The current in each resistor is the same when connected in parallel combination.
2. Then recognize the resistances connected in parallel and find the equivalent resistances of parallel combinations by summing the reciprocals of the resistances and then taking the reciprocal of the result. Draw the new, simplified circuit diagram.
(1/R)=(1/R_{1})+(1/R_{2})+(1/R_{2})
Remember that for resistors connected in parallel combination ‘The potential difference across each resistor is the same’.
3. Repeat the first two steps as required, until no further combinations can be made using resistances. If there is only a single battery in the circuit, this will usually result in a single equivalent resistor in series with the battery.
4. Use Ohm’s Law, V= IR, to determine the current in the equivalent resistor. Then work backwards through the diagrams, applying the useful facts listed in step 1 or step 2 to find the currents in the other resistors. (In more complex circuits, Kirchhoff’s rules can be applied).
For series combination of resistances equivalent resistance is given by the equation
R_{eq}= R_{1} + R_{2}+R_{3}
The current in each resistor is the same when connected in parallel combination.
2. Then recognize the resistances connected in parallel and find the equivalent resistances of parallel combinations by summing the reciprocals of the resistances and then taking the reciprocal of the result. Draw the new, simplified circuit diagram.
(1/R)=(1/R_{1})+(1/R_{2})+(1/R_{2})
Remember that for resistors connected in parallel combination ‘The potential difference across each resistor is the same’.
3. Repeat the first two steps as required, until no further combinations can be made using resistances. If there is only a single battery in the circuit, this will usually result in a single equivalent resistor in series with the battery.
4. Use Ohm’s Law, V= IR, to determine the current in the equivalent resistor. Then work backwards through the diagrams, applying the useful facts listed in step 1 or step 2 to find the currents in the other resistors. (In more complex circuits, Kirchhoff’s rules can be applied).
CSIR NET physics: Ferromagnetism (in short) Part 1
For reading ferromagnetism for higher level visit the link given below
CSIR NET physics: Ferromagnetism (in short) Part 1: "A ferromagnetic material has a spontaneous magnetic moment magnetic moment even in zero applied magnetic field this means that electron s..."
CSIR NET physics : Ferromagnetism (in short) part 2: "Nature of Ferromagnetic carriers : Entire magnetization must be essentially associated with electron spin, and not at all with the orbital motion of electrons....."
Hope you like it
physics expert
CSIR NET physics: Ferromagnetism (in short) Part 1: "A ferromagnetic material has a spontaneous magnetic moment magnetic moment even in zero applied magnetic field this means that electron s..."
CSIR NET physics : Ferromagnetism (in short) part 2: "Nature of Ferromagnetic carriers : Entire magnetization must be essentially associated with electron spin, and not at all with the orbital motion of electrons....."
Hope you like it
physics expert
Ferromagnetism (in short) Part 2
Nature of Ferromagnetic carriers
Origin of exchange interaction
Ferromagnetic domains
 Entire magnetization must be essentially associated with electron spin, and not at all with the orbital motion of electrons.
 Argon core (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}) of Fe , Co and Ni can be left out of account as a source of ferromagnetism.
 4s electrons are responsible for electrical conductivity and crystal binding.
 Thus 3d electrons with unpaired spins are responsible for magnetization of these metals.
 An effective number of magnetic moment carriers per atom should be non integral, despite that each atom has an integral number of electrons Fe  4 electrons : Co  3 electrons : Ni  2 electrons and each electron contributes a magnetic moment of 1μ_{B} due to spin alone.
 Above argument applies to free atom but here they are bound into solids where atomic levels are bounded into bands.
 Non integral values 2.22μ_{B}, 1.72μ_{B} and 0.54μ_{B} for Fe, Co, and Ni resp. of magnetic moment carriers which each atom supplies can be explained as follows : Wide 4s band of these metals overlaps with narrow 3d band. As a consequence , there is , on an average a certain fraction of total number of 3d plus 4s electrons in each band; the relative occupation of two bands being determined by fermi level E_{F}
Origin of exchange interaction
 Explanation of large value of molecular field is based on non magnetic interaction that is exchange interaction.
 Exchange interaction arises as a consequence of Pauli's Exclusion principle. Because of this principle we can not change the relative orientation of two spins without changing the spatial distribution of charge , clearly indicating that interaction exists between two atoms.
 This interaction depends on relative orientation of electron spins not on the magnetic moments.
 The energy of this interaction between atoms i , j bearing spins S_{i} , S_{j} is of the form E_{ex}=2J_{e}S_{i}.S_{j} where J_{e} is the exchange integral , its value is related to the overlap of the charge distribution of atoms i and j i.e., on their inter atomic separation.
 Energy of parallel configuration is lower than that of anti parallel by amount 2J_{e} this implies that former configuration is more stable favouring magnetization to occur.
 Note that exchange interaction is positive only for iron group and negative for others.
Ferromagnetic domains
 The fundamental problem of ferromagnetism is to explain why the elementary moments of a ferromagnetic material can be aligned so much more easily then those of paramagnetic materials.
 Weiss suggested that these were forces of interaction between elementary magnetic moments tending to make each one parallel to their neighbours.
 Such forces would cause all moments to be aligned in the same direction at absolute zero of temperature and this ordering of moments would continue when temperature is raised, though with increasing deviation from perfect alignment, until a critical temperature is reached , above which the moments are arranged in random, as in a paramagnetic material.
 Weiss theory can thus account for the fact that ferromagnetic materials may be spontaneously magnetized even in the absence of external magnetic field ; it does not explain why the majority of ferromagnetic are not actually found in this spontaneously magnetized state , but are much more likely to have zero magnetization.
 This difficulty can be met by introducing the hypothesis of domain theory.
 Here supposed that the forces of interaction only maintained the parallel alignment of elementary moments over fairly small regions .
 Actual specimen are composed of small regions called domains , within each of which the local magnetization is saturated.
 The direction of magnetization of different domains need not be parallel.
 The increase of gross magnetic moment of a ferromagnetic specimen in an applied magnetic field takes place by two independent processes : (1) In weak applied fields the volume of domains favorably oriented w.r.t. the field increases at the expense of unfavorably oriented domains (2) In strong applied fields the domain magnetization rotates towards the direction of the field.
Ferromagnetism (in short) Part 1
 A ferromagnetic material has a spontaneous magnetic moment magnetic moment even in zero applied magnetic field this means that electron spins and magnetic moments are arranged in regular manner.
 Consider a paramagnet with a concentration of N ions of spin S. Given an internal interaction tending to line up the magnetic moments parallel to each other , we shall have a ferromagnet.
 This internal interaction is called exchange field.
 Orienting effect of exchange field is opposed by thermal agitation.
 At elevated temperatures the spin order is destroyed.
 Exchange field can be treated as equivalent to BE (magnetic field) also assume that the exchange field B_{E} is proportional to the magnetization M.
 Magnetization M is defined as the magnetic moment per unit volume.
 In mean field approximation each magnetic atom experiences a field proportional to the magnetization
B_{E}=λM (1)
Where λ a is constant independent of temperature.  Each spin sees average magnetization of all the other spins and more precisely of the neighboring spins.
 Curie Temperature (T_{c}) is the temperature above which spontaneous magnetization vanishes.
 T_{c} separates disordered paramagnetic phase at temperature T > T_{c} from ordered ferromagnetic phase at temperature T < T_{c}.
 If B_{a} is the external magnetic field then the effective field acting on atom or ion is
B= B_{a}+ B_{E} = B_{a}+ λM  If χ_{p} is paramagnetic susceptibility then
M= χ_{p}( B_{a}+ B_{E})
χ_{p}=C/T from curie law for paramagnetic materials
this implies that MT=C(B_{a}+ λM)  Susceptibility has singularity at T=Cλ.
 At this temperature and below there exists a spontaneous magnetization , because if χ is infinite, we can have a finite M for zero B_{a}.
 CurieWeiss law is
χ=C/(TT_{c}) or T_{c}=Cλ  This spontaneous magnetization decreases very slowly as the temperature is first raised above absolute zero and drops more steeply at higher temperatures until finally falls to zero at curie temperature.
Radiology and Physics – Career Options and Other Important Aspects
Radiology and Physics – Career Options and Other Important Aspects Most people are familiar with the terms radiology and physics – the former is the branch of medicine that deals with the research in and application of imaging technologies for diagnostic and treatment purposes like Xrays, CT, MRI, PET, ultrasound and nuclear medicine, while the latter is a branch of science that deals with the properties of matter and energy and the relationships between them. Putting the two together, we get radiologic physics, a specialized branch of physics that has three fields: Therapeutic radiological physics – deals with the physical aspects of the therapeutic applications of Xrays, gamma rays, electron beams, charged particle beams, neutrons, and radiations from sealed radionuclide sources, the use of the equipment that produces them, and the safety aspects of using radiation in diagnostics and therapy. Diagnostic radiological physics – concerns the diagnostic applications of Xrays, gamma rays from sealed sources, ultrasonic radiation and magnetic resonance, the use of the equipment that produces them, and the safety aspects in using them for diagnostic and therapeutic purposes. Medical nuclear physics  is related to the therapeutic and diagnostic applications of radionuclides (from unsealed sources), the equipment associated with their production and use, and the safety aspects of radiation. You can choose to obtain certification from the American Board of Radiology (ABR) in one or more of the above areas of study. As a radiologic physicist, you are qualified to act in an advisory capacity to physicians regarding the physical aspects of radiation therapy, diagnostic radiation and/or nuclear medicine. You will be working directly with oncologists and physicians in planning the treatment of patients who require radiation therapy and in delivering the therapy using the right equipment. Besides this, you are also in charge developing and directing quality control programs for equipment and procedures; this means that you ensure that the equipment that delivers the radiation works properly and has been correctly calibrated and that you ensure that complicated therapy routines are tailored to the needs of each patient. You also supervise the work of dosimetrist (they work as part of oncology teams and analyze data to come up with the right course of therapy to deliver the right dosage of radiation to the right location, minimizing harm to neighboring organs and tissue). Radiologic physicists must have at least a master’s degree if they wish to find good jobs and challenging positions with healthcare centers, hospitals and research facilities.
This guest post is contributed by Rachel Davis, she writes on the topic Radiology programs. She welcomes your comments at her email id: racheldavis65@gmail.com.
This guest post is contributed by Rachel Davis, she writes on the topic Radiology programs. She welcomes your comments at her email id: racheldavis65@gmail.com.
Test Yourself (Miscellaneous MCQ's)
Qiestion 1
If relatibe permeability of iron is 5500 then its magnetic susceptibility is
(a) 5500 x 10^{7}
(b) 5501
(c) 5499
(d) 5500 x 10^{7}
Question 2
An atom is paramagnetic if it has
(a) an electric dipole moment
(b) no magnetic moment
(c) a magnetic moment
(d) no electric dipole moment
Question 3
Magnetic moment of a diamegnetic atim is
(a) 0
(b) infinity
(c) negative
(d) positive
Question 4
Mark the correct statement(s)
(a) When a particle moves under uniform circular motion its acceleration is constant
(b) Under the influence of uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(c) Under the influence of nonuniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(d) All the above
Qiestion 5
In a meter bridge apparatus , the bridge wire should have
(a) high resistivity and low temperature coefficent
(b) high resistivity and high temperature coefficent
(c) low resistivity and high temperature coefficent
(d) low resistivity and low temperature coefficent
Question 6
Mark out the correct statement
(a) Image formed by convex mirror can be real
(b) Image formed by convex mirror can be virtual
(c) Image formed by convex mirror can be magnified
(d) Image formed by convex mirror can be inverted
Answer
1. c
2. c
3. a
4. b .... When a particle moves under the influence of uniform circular motion magnitude of acceleration is always constant but direction of acceleration keeps changing, it always remains towards the centre . So acceleration is always perpandicular to the the tangential velocity in this case.
5. a
6. a,b,c,d
If relatibe permeability of iron is 5500 then its magnetic susceptibility is
(a) 5500 x 10^{7}
(b) 5501
(c) 5499
(d) 5500 x 10^{7}
Question 2
An atom is paramagnetic if it has
(a) an electric dipole moment
(b) no magnetic moment
(c) a magnetic moment
(d) no electric dipole moment
Question 3
Magnetic moment of a diamegnetic atim is
(a) 0
(b) infinity
(c) negative
(d) positive
Question 4
Mark the correct statement(s)
(a) When a particle moves under uniform circular motion its acceleration is constant
(b) Under the influence of uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(c) Under the influence of nonuniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(d) All the above
Qiestion 5
In a meter bridge apparatus , the bridge wire should have
(a) high resistivity and low temperature coefficent
(b) high resistivity and high temperature coefficent
(c) low resistivity and high temperature coefficent
(d) low resistivity and low temperature coefficent
Question 6
Mark out the correct statement
(a) Image formed by convex mirror can be real
(b) Image formed by convex mirror can be virtual
(c) Image formed by convex mirror can be magnified
(d) Image formed by convex mirror can be inverted
Answer
1. c
2. c
3. a
4. b .... When a particle moves under the influence of uniform circular motion magnitude of acceleration is always constant but direction of acceleration keeps changing, it always remains towards the centre . So acceleration is always perpandicular to the the tangential velocity in this case.
5. a
6. a,b,c,d
Prepare yourself for Competetive Exams
This time is mid of the november and can prove deciding time for those preparing for competetive examinations like IITJEE/PMT/AIEEE etc and various other examinations. Ideally you should nearly complete all your syllabus by this month and if you have not completed it then try to cover the syllabus quickly by the end of this month. After you have completed all your syllabus then start revising it keeping yourself cool and calm.
Try an explore all the topics of your syllabus for the competetive exams. After having looked up and revised complete syllabus you should start practicing simulated exame type situations to increase your confidence there are various websites online where you can take such tests.
So all the best for the preparations of your competetive exams. Stop panicing if you have little time left and large portions to cover just fix your goals and start preparing.
Try an explore all the topics of your syllabus for the competetive exams. After having looked up and revised complete syllabus you should start practicing simulated exame type situations to increase your confidence there are various websites online where you can take such tests.
So all the best for the preparations of your competetive exams. Stop panicing if you have little time left and large portions to cover just fix your goals and start preparing.
Comparison between Coulomb’s laws and Biot Savart laws
1. Both the electric and magnetic field depends inversely on square of distance between the source and field point .Both of them are long range forces
2. Charge element dq producing electric field is a scalar whereas the current element Idl is a vector quantity having direction same as that of flow of current
3. According to coulomb’s law ,the magnitude of electric field at any point P depends only on the distance of the charge element from any point P .According to Biot savart law ,the direction of magnetic field is perpendicular to the current element as well as to the line joining the current element to the point P
4. Both electric field and magnetic field are proportional to the source strength namely charge and current element respectively. This linearity makes it simple to find the field due to more complicated distribution of charge and current by superposing those due to elementary changes and current elements
2. Charge element dq producing electric field is a scalar whereas the current element Idl is a vector quantity having direction same as that of flow of current
3. According to coulomb’s law ,the magnitude of electric field at any point P depends only on the distance of the charge element from any point P .According to Biot savart law ,the direction of magnetic field is perpendicular to the current element as well as to the line joining the current element to the point P
4. Both electric field and magnetic field are proportional to the source strength namely charge and current element respectively. This linearity makes it simple to find the field due to more complicated distribution of charge and current by superposing those due to elementary changes and current elements
Electrostatics : Very Short answer type questions
Question 1: Define following terms
(a) Dielectric constant of a medium
(b) Electric dipole moment
(c) Electric flux
Answer 1:
(a)It is the ratio of the capacitance (C_{r}) of a capacitor with dielectric between the plates to the capacitance (C_{r}) of the same capacitor with vacuum between the plates i.e. K=C_{r}/C_{0}
(b) It is the product of the magnitude of one of the point charges constitting the dipole ant the distance of separation between two point charges.
(c) Electric flux through an area is the product of the magnitude of the area and the component of electric field vector normal to this area element.
Electric flux = E.ds
SI unit of flux is NC^{1}m^{2}
Question 2: Electric field inside a dielectric decreases when it is placed in an external field. Give reason to support this statement.
Answer 2: An electric field E_{P} is induced inside the dielectric in a direction opposite to the direction of external electric field E_{0}. Thus net field becomes
E=E_{0}E_{P}
Question 3: Electric field lines can not be discontinuous. Give reason.
Answer 3: Electric field lines can not be discontinous because if they are discontinous then it will indicate the absence of electric field at the break point.
Question 4: Why do electric field lines can never cross each other?
Answer 4: It is so because if they cross each other then at the point of intersection there will be two tangents which is not possible.
Question 5: What is the net amount of charge on a charged capacitor?
Answer 5: The net charge of a charged capacitor is zero because the charges on its two plates are equal in number and opposite in sign. Even when the capacitor is discharged net charge of the capacitor remains zero because then each plate has zero charge.
(a) Dielectric constant of a medium
(b) Electric dipole moment
(c) Electric flux
Answer 1:
(a)It is the ratio of the capacitance (C_{r}) of a capacitor with dielectric between the plates to the capacitance (C_{r}) of the same capacitor with vacuum between the plates i.e. K=C_{r}/C_{0}
(b) It is the product of the magnitude of one of the point charges constitting the dipole ant the distance of separation between two point charges.
(c) Electric flux through an area is the product of the magnitude of the area and the component of electric field vector normal to this area element.
Electric flux = E.ds
SI unit of flux is NC^{1}m^{2}
Question 2: Electric field inside a dielectric decreases when it is placed in an external field. Give reason to support this statement.
Answer 2: An electric field E_{P} is induced inside the dielectric in a direction opposite to the direction of external electric field E_{0}. Thus net field becomes
E=E_{0}E_{P}
Question 3: Electric field lines can not be discontinuous. Give reason.
Answer 3: Electric field lines can not be discontinous because if they are discontinous then it will indicate the absence of electric field at the break point.
Question 4: Why do electric field lines can never cross each other?
Answer 4: It is so because if they cross each other then at the point of intersection there will be two tangents which is not possible.
Question 5: What is the net amount of charge on a charged capacitor?
Answer 5: The net charge of a charged capacitor is zero because the charges on its two plates are equal in number and opposite in sign. Even when the capacitor is discharged net charge of the capacitor remains zero because then each plate has zero charge.
Wave Optics : Part 2
 In Young’s Experiment two parallel and very close slits S1and S2 (illuminated by other another narrow slit) behaves like two coherent sources and produces a pattern of dark and bright bands (interference fringes) on a screen. For a point P on the screen
S2PS1P≈y1d/D1
Where d is the separation distance between two slits, D1 is the distance between the slits and the screen and y1 is the distance of point P from the central fringe.
 For constructive interference (bright band) , the path difference must be an integral multiple of wavelength λ i.e.,
y1d/D1 = n λ or y1=nD1λ/d
 The separation distance Δy1 between adjacent bright or dark fringes is
Δy1 = D1λ/d
Using this relation we can calculate wavelength λ.
 The colors shown by thin films are due to interference between two beams , one reflected from the top surface of the film and other from the bottom. The path difference between the two may give constructive interference for one color and destructive interference for another. Hence the reflected light is colored.
 Term diffraction refers to light spreading out from narrow holes and slits, and bending around corners and obstacles.
 The single slit diffraction pattern shows the central maximum (θ=0) at angular separation θ=±n λ (n≠0) and secondary maxima at θ=±(n+1/2) λ (n≠0).
 Different parts of the wave front at the slit acts as secondary sources ; diffraction pattern is the result of interference of waves from these sources.
 An aperture of size a sends diffracted light into an angle ≈ λ/a.
 Doppler effect is the shift in frequency of light when there is a relative motion between the source and the observer. It is given by
Δν/ν ≈ vr/c for v/c << 1
Where vr is the radial component of relative velocity v. This effect can be used to measure the speed of an approaching or receding object.
 Polarization specifies the manner in which electric field E oscillates in the plane transverse to direction of propagation of light. If E oscillates back and forth in a straight line , the wave is said to be linearly polarized. If the direction of E changes irregularly then the wave is unpolarized.
Wave velocity in a continuous system
For post on velocity of waves in continous medium visit the link given below
CSIR NET physics: Wave velocity in a continuous system: "Any system whose particle motion are governed by classical wave equation is a system in which harmonic waves of any wavelength can travel w..."
physicsexpert
CSIR NET physics: Wave velocity in a continuous system: "Any system whose particle motion are governed by classical wave equation is a system in which harmonic waves of any wavelength can travel w..."
physicsexpert
Wave velocity in a continuous system
 Any system whose particle motion are governed by classical wave equation is a system in which harmonic waves of any wavelength can travel with the speed v
 The value of v depends on the elastic and inertial properties of the system under consideration.
(1) Transverse wave on a stretched string
 Displacement of the string is governed by the equation
Where T is the tension and µ is the linear density (mass per unit length of the string)  Velocity of wave on the string is
v=√(T/μ)
v is the velocity of the wave.  Medium through which waves travel will offer impedance to these waves.
 If the medium is loss less i.e., it does not have any resistive or dissipative components, the impedance is solely determined by its inertia and elasticity.
 Characteristic impedance of string is determined by
Z=T/v=√(μT)=μv  Since v is determined by the inertia and elasticity this shows that impedance is also governed by these two properties of the medium.
 For lossless medium impedance is real quantity and it is complex if the medium is dissipative.
(2) Longitudinal waves in uniform rod
 Equation for longitudinal vibrations of a uniform rod is
 where ξ (x,t )→displacement
Y is young’s modulus of the rod
ρ is the density  Velocity of longitudinal wave in rod is
v=√(Y/ρ)
(3) Electromagnetic waves in space
 When electric and magnetic field vary in time they produce EM waves.
 An oscillating charge has an oscillating electric and magnetic fields around it and hence produces EM waves.
 Example:  (1) Electrons falling from higher to lower energy orbit radiates EM waves of particular wavelength and frequency. (2) The motion of electrons in an antenna radiates EM waves by a process called Bramstrhlung.
 Propagation of EM waves in a medium is also due to inertial and elastic properties of the medium.
 Every medium (including vacuum) has inductive properties described by magnetic permeability µ of the medium.
 This property provides magnetic inertia of the medium.
 Elasticity of the medium is provided by the capacitive property called electrical permittivity ε of the medium.
 Permeability µ stores magnetic energy and the permittivity ε stores the electric field energy.
 This EM energy propagates in the medium in the form of EM waves.
 Electric and magnetic fields are connected by Maxwell’s Equations (dielectric medium)
∇×H =ε (∂E )/∂t
∇×E =  μ (∂H⃗)/∂t
ε(∇∙E⃗)=ρ
∇∙H =0  Here in above equations E ⃗ is electric field , H ⃗ is the magnetic field and ρ is charge density
Color code of carbon resistance
• Commercially resistors of different type and values are available in the market but in electronic circuits carbon resistors are more frequently used
• In carbon resistors value of resistance is indicated by four colored bands marked on its surface as shown below in figure
• The first three bands a,b.c determine the value of the resistance and fourth band d gives the tolerance of the resistance
• The color of the first and second band respectively gives the first and second significant figure of the resistance and third band c gives the power of the ten by which two significant digits are multiplied for obtaining the value of the resistance
• value of different colors for making bands in carbon resistors are given below in the table
Color Figure(first and second band) Multiplier(for third band) tolerance
• For example in a given resistor let first strip be brown ,second strip be red and third be orange and fourth be gold then resistance of the resistor would be 12 x 10^{3} (± 5%
For more notes in physics visit physicscatalyst.com
• In carbon resistors value of resistance is indicated by four colored bands marked on its surface as shown below in figure
• The first three bands a,b.c determine the value of the resistance and fourth band d gives the tolerance of the resistance
• The color of the first and second band respectively gives the first and second significant figure of the resistance and third band c gives the power of the ten by which two significant digits are multiplied for obtaining the value of the resistance
• value of different colors for making bands in carbon resistors are given below in the table
Color Figure(first and second band) Multiplier(for third band) tolerance
• For example in a given resistor let first strip be brown ,second strip be red and third be orange and fourth be gold then resistance of the resistor would be 12 x 10^{3} (± 5%
For more notes in physics visit physicscatalyst.com
SYLLABUS FOR PHYSICAL SCIENCES PAPER I AND PAPER II
The full Syllabus for Part B of Paper I and Part B of Paper II.
The syllabus for Part A of Paper II comprises Sections IVI.
I. Mathematical Methods of Physics
Dimensional analysis; Vector algebra and vector calculus; Linear algebra, matrices, Cayley Hamilton theorem, eigenvalue problems; Linear differential equations; Special functions (Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier and Laplace transforms; Elements of complex analysis: Laurent seriespoles, residues and evaluation of integrals; Elementary ideas about tensors; Introductory group theory, SU(2), O(3); Elements of computational techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, solution of first order differential equations using RungeKutta method; Finite difference methods; Elementary probability theory, random variables, binomial, Poisson and normal distributions.
II. Classical Mechanics
Newton’s laws; Phase space dynamics, stability analysis; Centralforce motion; Twobody collisions, scattering in laboratory and centreofmass frames; Rigid body dynamics, moment of inertia tensor, noninertial frames and pseudoforces; Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and canonical transformations; Symmetry, invariance and conservation laws, cyclic coordinates; Periodic motion, small oscillations and normal modes; Special theory of relativity, Lorentz transformations, relativistic kinematics and mass–energy equivalence.
III. Electromagnetic Theory
Electrostatics: Gauss’ Law and its applications; Laplace and Poisson equations, boundary value problems; Magnetostatics: BiotSavart law, Ampere's theorem, electromagnetic induction; Maxwell's equations in free space and linear isotropic media; boundary conditions on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves in free space, dielectrics, and conductors; Reflection and refraction, polarization, Fresnel’s Law, interference, coherence, and diffraction; Dispersion relations in plasma; Lorentz invariance of Maxwell’s equations; Transmission lines and wave guides; Dynamics of charged particles in static and uniform electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials.
IV. Quantum Mechanics
Waveparticle duality; Wave functions in coordinate and momentum representations; Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac’s bra and ket notation; Schroedinger equation (timedependent and timeindependent); Eigenvalue problems such as particleinabox, harmonic oscillator, etc.; Tunneling through a barrier; Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin; Addition of angular momenta; Hydrogen atom, spinorbit coupling, fine structure; Timeindependent perturbation theory and applications; Variational method; WKB approximation;
Time dependent perturbation theory and Fermi's Golden Rule; Selection rules; Semiclassical theory of radiation; Elementary theory of scattering, phase shifts, partial waves, Born approximation; Identical particles, Pauli's exclusion principle, spinstatistics connection; Relativistic quantum mechanics: Klein Gordon and Dirac equations.
V. Thermodynamic and Statistical Physics
Laws of thermodynamics and their consequences; Thermodynamic potentials, Maxwell relations; Chemical potential, phase equilibria; Phase space, micro and macrostates; Microcanonical, canonical and grandcanonical ensembles and partition functions; Free Energy and connection with thermodynamic quantities; First and secondorder phase transitions; Classical and quantum statistics, ideal Fermi and Bose gases; Principle of detailed balance; Blackbody radiation and Planck's distribution law; BoseEinstein condensation; Random walk and Brownian motion; Introduction to nonequilibrium processes; Diffusion equation.
VI. Electronics
Semiconductor device physics, including diodes, junctions, transistors, field effect devices, homo and heterojunction devices, device structure, device characteristics, frequency dependence and applications; Optoelectronic devices, including solar cells, photodetectors, and LEDs; Highfrequency devices, including generators and detectors; Operational amplifiers and their applications; Digital techniques and applications (registers, counters, comparators and similar circuits); A/D and D/A converters; Microprocessor and microcontroller basics.
VII. Experimental Techniques and data analysis
Data interpretation and analysis; Precision and accuracy, error analysis, propagation of errors, least squares fitting, linear and nonlinear curve fitting, chisquare test; Transducers (temperature, pressure/vacuum, magnetic field, vibration, optical, and particle detectors), measurement and control; Signal conditioning and recovery, impedance matching, amplification (Opamp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding; Fourier transforms; lockin detector, boxcar integrator, modulation techniques.
Applications of the above experimental and analytical techniques to typical undergraduate and graduate level laboratory experiments.
VIII. Atomic & Molecular Physics
Quantum states of an electron in an atom; Electron spin; SternGerlach experiment; Spectrum of Hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; Zeeman, Paschen Back & Stark effect; Xray spectroscopy; Electron spin resonance, Nuclear magnetic resonance, chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic molecules; Frank – Condon principle and selection rules; Spontaneous and stimulated emission, Einstein A & B coefficients; Lasers, optical pumping, population inversion, rate equation; Modes of resonators and coherence length.
IX. Condensed Matter Physics
Bravais lattices; Reciprocal lattice, diffraction and the structure factor; Bonding of solids; Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific heat; Response and relaxation phenomena; Drude model of electrical and thermal
conductivity; Hall effect and thermoelectric power; Diamagnetism, paramagnetism, and ferromagnetism; Electron motion in a periodic potential, band theory of metals, insulators and semiconductors; Superconductivity, type – I and type  II superconductors, Josephson junctions; Defects and dislocations; Ordered phases of matter, translational and orientational order, kinds of liquid crystalline order; Conducting polymers; Quasicrystals.
X. Nuclear and Particle Physics
Basic nuclear properties: size, shape, charge distribution, spin and parity; Binding energy, semiempirical mass formula; Liquid drop model; Fission and fusion; Nature of the nuclear force, form of nucleonnucleon potential; Chargeindependence and chargesymmetry of nuclear forces; Isospin; Deuteron problem; Evidence of shell structure, single particle shell model, its validity and limitations; Rotational spectra; Elementary ideas of alpha, beta and gamma decays and their selection rules; Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; Classification of fundamental forces; Elementary particles (quarks, baryons, mesons, leptons); Spin and parity assignments, isospin, strangeness; GellMannNishijima formula; C, P, and T invariance and applications of symmetry arguments to particle reactions, parity nonconservation in weak interaction; Relativistic kinematics.
The syllabus for Part A of Paper II comprises Sections IVI.
I. Mathematical Methods of Physics
Dimensional analysis; Vector algebra and vector calculus; Linear algebra, matrices, Cayley Hamilton theorem, eigenvalue problems; Linear differential equations; Special functions (Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier and Laplace transforms; Elements of complex analysis: Laurent seriespoles, residues and evaluation of integrals; Elementary ideas about tensors; Introductory group theory, SU(2), O(3); Elements of computational techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, solution of first order differential equations using RungeKutta method; Finite difference methods; Elementary probability theory, random variables, binomial, Poisson and normal distributions.
II. Classical Mechanics
Newton’s laws; Phase space dynamics, stability analysis; Centralforce motion; Twobody collisions, scattering in laboratory and centreofmass frames; Rigid body dynamics, moment of inertia tensor, noninertial frames and pseudoforces; Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and canonical transformations; Symmetry, invariance and conservation laws, cyclic coordinates; Periodic motion, small oscillations and normal modes; Special theory of relativity, Lorentz transformations, relativistic kinematics and mass–energy equivalence.
III. Electromagnetic Theory
Electrostatics: Gauss’ Law and its applications; Laplace and Poisson equations, boundary value problems; Magnetostatics: BiotSavart law, Ampere's theorem, electromagnetic induction; Maxwell's equations in free space and linear isotropic media; boundary conditions on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves in free space, dielectrics, and conductors; Reflection and refraction, polarization, Fresnel’s Law, interference, coherence, and diffraction; Dispersion relations in plasma; Lorentz invariance of Maxwell’s equations; Transmission lines and wave guides; Dynamics of charged particles in static and uniform electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials.
IV. Quantum Mechanics
Waveparticle duality; Wave functions in coordinate and momentum representations; Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac’s bra and ket notation; Schroedinger equation (timedependent and timeindependent); Eigenvalue problems such as particleinabox, harmonic oscillator, etc.; Tunneling through a barrier; Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin; Addition of angular momenta; Hydrogen atom, spinorbit coupling, fine structure; Timeindependent perturbation theory and applications; Variational method; WKB approximation;
Time dependent perturbation theory and Fermi's Golden Rule; Selection rules; Semiclassical theory of radiation; Elementary theory of scattering, phase shifts, partial waves, Born approximation; Identical particles, Pauli's exclusion principle, spinstatistics connection; Relativistic quantum mechanics: Klein Gordon and Dirac equations.
V. Thermodynamic and Statistical Physics
Laws of thermodynamics and their consequences; Thermodynamic potentials, Maxwell relations; Chemical potential, phase equilibria; Phase space, micro and macrostates; Microcanonical, canonical and grandcanonical ensembles and partition functions; Free Energy and connection with thermodynamic quantities; First and secondorder phase transitions; Classical and quantum statistics, ideal Fermi and Bose gases; Principle of detailed balance; Blackbody radiation and Planck's distribution law; BoseEinstein condensation; Random walk and Brownian motion; Introduction to nonequilibrium processes; Diffusion equation.
VI. Electronics
Semiconductor device physics, including diodes, junctions, transistors, field effect devices, homo and heterojunction devices, device structure, device characteristics, frequency dependence and applications; Optoelectronic devices, including solar cells, photodetectors, and LEDs; Highfrequency devices, including generators and detectors; Operational amplifiers and their applications; Digital techniques and applications (registers, counters, comparators and similar circuits); A/D and D/A converters; Microprocessor and microcontroller basics.
VII. Experimental Techniques and data analysis
Data interpretation and analysis; Precision and accuracy, error analysis, propagation of errors, least squares fitting, linear and nonlinear curve fitting, chisquare test; Transducers (temperature, pressure/vacuum, magnetic field, vibration, optical, and particle detectors), measurement and control; Signal conditioning and recovery, impedance matching, amplification (Opamp based, instrumentation amp, feedback), filtering and noise reduction, shielding and grounding; Fourier transforms; lockin detector, boxcar integrator, modulation techniques.
Applications of the above experimental and analytical techniques to typical undergraduate and graduate level laboratory experiments.
VIII. Atomic & Molecular Physics
Quantum states of an electron in an atom; Electron spin; SternGerlach experiment; Spectrum of Hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; Zeeman, Paschen Back & Stark effect; Xray spectroscopy; Electron spin resonance, Nuclear magnetic resonance, chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic molecules; Frank – Condon principle and selection rules; Spontaneous and stimulated emission, Einstein A & B coefficients; Lasers, optical pumping, population inversion, rate equation; Modes of resonators and coherence length.
IX. Condensed Matter Physics
Bravais lattices; Reciprocal lattice, diffraction and the structure factor; Bonding of solids; Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific heat; Response and relaxation phenomena; Drude model of electrical and thermal
conductivity; Hall effect and thermoelectric power; Diamagnetism, paramagnetism, and ferromagnetism; Electron motion in a periodic potential, band theory of metals, insulators and semiconductors; Superconductivity, type – I and type  II superconductors, Josephson junctions; Defects and dislocations; Ordered phases of matter, translational and orientational order, kinds of liquid crystalline order; Conducting polymers; Quasicrystals.
X. Nuclear and Particle Physics
Basic nuclear properties: size, shape, charge distribution, spin and parity; Binding energy, semiempirical mass formula; Liquid drop model; Fission and fusion; Nature of the nuclear force, form of nucleonnucleon potential; Chargeindependence and chargesymmetry of nuclear forces; Isospin; Deuteron problem; Evidence of shell structure, single particle shell model, its validity and limitations; Rotational spectra; Elementary ideas of alpha, beta and gamma decays and their selection rules; Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; Classification of fundamental forces; Elementary particles (quarks, baryons, mesons, leptons); Spin and parity assignments, isospin, strangeness; GellMannNishijima formula; C, P, and T invariance and applications of symmetry arguments to particle reactions, parity nonconservation in weak interaction; Relativistic kinematics.
Blog for graduate level physics: Waves in continous medium
Hi all
For a detailed post on waves visit
Blog for graduate level physics: Waves in continous medium: "There are essentially two ways of transporting energy from one place to another (a) Actual transport of matter for example a fired bullet an..."
Thank you
physicsexpert
For a detailed post on waves visit
Blog for graduate level physics: Waves in continous medium: "There are essentially two ways of transporting energy from one place to another (a) Actual transport of matter for example a fired bullet an..."
Thank you
physicsexpert
Waves in continous medium
 There are essentially two ways of transporting energy from one place to another (a) Actual transport of matter for example a fired bullet and (b) Waves carry energy but there is no transport of matter for example sound waves carry energy so thay can move diphagram of the ear.
 Here we will consider the oscillations of open or unbounded systems i.e., systems having no outer boundaries.
 If such system is disturbed , waves travel in the system with a speed determined by the properties of the system.
 Waves are not reflected back in such a system.
 The waves generated by driving force are called travelling waves ; these waves travel from the point where the driving force produces the disturbance.
 If the driving force produces a harmonic disturbance the travelling wave it produces are called harmonic travelling waves.
 In the steady state, all moving parts of the system oscillates with simple harmonic motion at the driving frequency.
 Waves where the displacements or oscillations are transverse (i.e., perpandicular) to the direction of wave propagation is called transverse wave.
 The wavelength (denoted by λ) of the wave is defined as the distance, measured along the direction of the propagation of the wave, between two nearest points which are in the same state of viberation.
 Wavelength λ is just the distance travelled by the wave during one time period T of particle oscillation. Thus wave velocity
v=λ/T=λν
where ν=1/T  is the frequency of the wave.  This relation between wave velocity, frequency and wavelength also holds for longitudinal waves in which the displacements or oscillation in the medium are parallel to the direction of wave propagation.
 Waves in spring and sound waves are longitudinal waves.
 Wavelength for longitudinal waves is the distance between two successive compressions or rarefactions.
 Sound waves are also compressional.
 Assumptions that are made while obtaining wave equation are:
1. Amplitude A of particle oscillations does not change in course of the propagation of wave.
2. The medium is isotopic and homogeneous so that velocity of wave does not chance from place to place  Displacement of particle at x at any time t is
Ψ(x,t) = A sin{2π(tx/v)/T)}  The function Ψ(x,t) repeats itself in a distance λ . Wavelength of a wave is also known as spatial periodicity of the wave.
 The wave is thus doubly periodic. It has temporal periodicity T and spatial periodicity λ.
 Let us define quantities
k=2π/λ and
ω=2π/T
then wave function can be written as
Ψ(x,t) = A sin{ωtkx}
where quantity k is known as wave number of the wave and ω is called angular frequency of particle oscillations in wave.  Harmonic wave travelling in
+ x direction : Ψ(x,t) = A sin{ωtkx}
 x direction : Ψ(x,t) = A sin{ωt+kx}
above equations can also be equally well described by cosine function.  Classicsl wave equation is
 Important inferences from above wave equation
1. Whenever second order time derivative of any physical quantity is related to second order space derivative as in above equation , a wave of some sort must travell in the medium.
2. Velocity of that wave is given by the square root of the coefficent of second order space derivative.  Individual derivatives which makes up the medium do not propagate through the medium with the wave; they merely oscillates ( transversly or longitudinally) about there equilibrium positions.
 It is their phase relationship which we observe as wave.
 Wave velocity is also called phase velocity with which crest or troughs in case of transverse wave and compressions or rarefactions in case of longitudinal waves travell through the medium.
 The phase velocity is given by
v=λ/T=λν
or,
v=ω/k  Ψ(x,t)=f(vtx) is the solution of the above given wave equation.
Wave Optics : Part 1
1. A wavefront is the locus of points having same phase of oscillation.
2. Rays are lines perpandicular to the wavefront, which shows the direction of propagation of energy.
3. The time taken for light to travel from one wavefront to another is same along any ray.
4. Huygen's construction is based on the principle that every point of a wavefront is the source of secondary wavefront that is the surface tangent to all secondary wavefronts gives rise to a new wavefront.
5. The law of refraction (i=r) and the Snell's law of refraction
sini /sinr =v_{1}/v_{2}=n_{2}/n_{1} = n_{21}
can be derived using the wave theory. Here v_{1} and v_{2} are the speed of light in media 1 and 2 wiyh refractive index n_{1} and n_{2} respectively.
6. The frequency ν remains same when light travels from one medium to another. The speed of the wave is given by
v=λ/T=λν
where λ is the wavelength of the wave and T is the period of oscillation.
7. Emission , absorption and scattering are the three proscesses by which matter interacts with radiation.
8. In emission , an accelerated charge radiates an looses energy.
9. In absorption the charge gains energy at the expence of the EM wave.
10. In scattering the charge accelerated by incident EM wave radiated in all direction.
11. Two sources of light are coherent if they have same frequency and stable phase difference.
12. In case of coherent sources of light the total intensity I is not just the sum of individual intensities I_{1} and I_{2} due to two sources but also includes an interference term that is
I = I_{1} + I_{2} + 2kE_{1}.E_{2}
where E_{1} and E_{2} are the electric fields at a point due to the sources.
13. The interference term averaged over many cycles is zero if (i) the source of light have different frequencies or (ii) the source have the same frequency but not stable phase difference. For such incoherent sources I = I_{1} + I_{2}
2. Rays are lines perpandicular to the wavefront, which shows the direction of propagation of energy.
3. The time taken for light to travel from one wavefront to another is same along any ray.
4. Huygen's construction is based on the principle that every point of a wavefront is the source of secondary wavefront that is the surface tangent to all secondary wavefronts gives rise to a new wavefront.
5. The law of refraction (i=r) and the Snell's law of refraction
sini /sinr =v_{1}/v_{2}=n_{2}/n_{1} = n_{21}
can be derived using the wave theory. Here v_{1} and v_{2} are the speed of light in media 1 and 2 wiyh refractive index n_{1} and n_{2} respectively.
6. The frequency ν remains same when light travels from one medium to another. The speed of the wave is given by
v=λ/T=λν
where λ is the wavelength of the wave and T is the period of oscillation.
7. Emission , absorption and scattering are the three proscesses by which matter interacts with radiation.
8. In emission , an accelerated charge radiates an looses energy.
9. In absorption the charge gains energy at the expence of the EM wave.
10. In scattering the charge accelerated by incident EM wave radiated in all direction.
11. Two sources of light are coherent if they have same frequency and stable phase difference.
12. In case of coherent sources of light the total intensity I is not just the sum of individual intensities I_{1} and I_{2} due to two sources but also includes an interference term that is
I = I_{1} + I_{2} + 2kE_{1}.E_{2}
where E_{1} and E_{2} are the electric fields at a point due to the sources.
13. The interference term averaged over many cycles is zero if (i) the source of light have different frequencies or (ii) the source have the same frequency but not stable phase difference. For such incoherent sources I = I_{1} + I_{2}
Overview of electrostatics and electricity
For a note on overview of electrostatics and electricity click the link given below:
Overview of electrostatics and electricity:
"Electrostatics involves electric charges namely positive and negative charges, the forces between them which is known as electric force , th..."
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Overview of electrostatics and electricity:
"Electrostatics involves electric charges namely positive and negative charges, the forces between them which is known as electric force , th..."
Hope you like the post
Concept of force
 Concept of force is central to all of physics whether it is classical physics,nuclear physics,quantum physics or any other form of physics
 So what is force? when we push or pull anybody we are said to exert force on the body
 Push or pull applied on a body does not exactly define the force in general.We can define force as an influence causing a body at rest or moving with constant velocity to undergo an accleration
 There are many ways in which one body can exert force on another body
Few examples are given below
(a)Stretched springs exerts force on the bodies attached to its ends
(b)Compressed air in a container exerts force on the walls of the container
(c) Force can be used to deform a flexible object
There are lots of examples you could find looking around yourself  Force of gravitational attraction exerted by earth is a kind of force that acts on every physical body on the earth and is called the weight of the body
 Mechanical and gravitation forces are not the only forces present infact all the forces in Universe are based on four fundamental forces
(i) Strong and weak forces: These are forces at very short distance (10^{05} m) and are responsible for interaction between neutrons and proton in atomic nucleus
(ii) Electromagnetic forces: EM force acts between electric charges
(iii) Gravitational force it acts between the masses  In mechanics we will only study about the mechanical and gravitational forces
 Force is a vector quatity and it needs both the magnitude as well as direction for its complete description
 SI unit of force is Newton (N) and CGS unit is dyne where
1 dyne= 10^{05} N
Uncertainity Principle
Hi all this post is for those who are interested in higher level physics. To view this post click the link given below.
Uncertainity Principle: "Uncertainity principle says that 'If a measurement of position is made with accuracy Δx and if the measurement of momentum is made simultane..."
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PhysicsExpert
Uncertainity Principle: "Uncertainity principle says that 'If a measurement of position is made with accuracy Δx and if the measurement of momentum is made simultane..."
hope you like it
PhysicsExpert
Uncertainity Principle
Uncertainity principle says that "If a measurement of position is made with accuracy Δx and if the measurement of momentum is made simultaneously with accuracy Δp , then the product of two errors can never be smaller than a number of order h
ΔpΔx≥(∼h) (1)
Similarly if the energy of the syatem is measured to accuracy ΔE , then time to which this measurement refers must have a minimum uncertainity given by
ΔEΔt≥(∼h) (2)
In generalised sence we can say that if Δq is the error in the measurement of any coordinate and Δp is the error in its canonically conjugate momentum then we have,
ΔpΔq≥(∼h) (3)
Consider the relation between the range of position Δx and range of wave number Δk appearing in a wave packet then
ΔxΔk≥1 (4)
and this is a general property not restricted to quantum mechanics. Uncertainity principle is obtaines when the following quantum mechanical interpretation of quantities appearing in above equation are taken into account.
(1) The deBrogli equation p=hk creates a relationship between wave number and momentum , which is not present in classical mechanics.
(2) Whenever either the momentum or the position of an electron is measured , the result is always some definite number. A classical wave packet always covers a range of positions and range of wave numbers.
Δx is a measure of minimum uncertainity or lack of complete determination of the position that can be ascribed to the electron. and Δk is the measure of minimum uncertainity or lack of complete determination of the momentum that can be ascribed to it.
Relation of spreading wave packet to uncertainity principle
Narrower the wave packet to begin with , the more rapidly it spreads. Because of the confinement of the packet within the region Δx_{0} the fourier analysis contains many waves of length of order of Δx_{0} , hence momenta p≅h/Δx_{0}
therefore
Δv≅p/m≅h/mΔx_{0}
Although average velocity of the packet is equal to the group velocity , there is still a strong chance that the actual velocity will fluctuate about this average by the same amount. The distance covered by the particle is not completely determined but it may vary as much as
Δx≅tΔv≅ht/mΔx_{0}
The spread of the wave packet may therefore be regarded as one of the manifestations of the lack of complete determination of initial velocity necesarily associated with the narrow wave packet.
Relation of stability of atom to uncertainity principle
From uncertainity principle if an electron is localized it must have on an average a high momentum and have high kinetic energy as it takes energy to localize a particle. According to uncertainity principle it takes a momentum Δp≅h/Δx and an energy nearly equal to h^{2}/2m(Δx)^{2} to keep an electron localised within a region Δx. Momentum creates a pressure which tends to oppose localization of the electron. In an atom the pressure is opposed by the force attracting the electron back to the nucleus. Thus the electron will come to equilibrium when the attractive forces balances the effective pressure and, this way , the mean radius of the lowest quantum state is determined. This point of balance can be found from the condition that total energy must be minimum. Thus we have
W≅ (h^{2}/2m(Δx)^{2})  (e^{2}/Δx)
Differentiating both the sides w.r.t. Δx and making ∂W/∂(Δx) = 0 we get
Δx≅h^{2}/me^{2}
THis result is just the radius of first Bohr orbit although not exact but qualitative.. The limitation of the localizability of the electron is inherent in the waveparticle nature of matter. In order to have an electron in very small space , we must have very high fourier components in its wave function and therefore the possibility of very high moments. There is no way to force an electron to occpy a well defined position and still remain at rest.
ΔpΔx≥(∼
Similarly if the energy of the syatem is measured to accuracy ΔE , then time to which this measurement refers must have a minimum uncertainity given by
ΔEΔt≥(∼
In generalised sence we can say that if Δq is the error in the measurement of any coordinate and Δp is the error in its canonically conjugate momentum then we have,
ΔpΔq≥(∼
Consider the relation between the range of position Δx and range of wave number Δk appearing in a wave packet then
ΔxΔk≥1 (4)
and this is a general property not restricted to quantum mechanics. Uncertainity principle is obtaines when the following quantum mechanical interpretation of quantities appearing in above equation are taken into account.
(1) The deBrogli equation p=
(2) Whenever either the momentum or the position of an electron is measured , the result is always some definite number. A classical wave packet always covers a range of positions and range of wave numbers.
Δx is a measure of minimum uncertainity or lack of complete determination of the position that can be ascribed to the electron. and Δk is the measure of minimum uncertainity or lack of complete determination of the momentum that can be ascribed to it.
Relation of spreading wave packet to uncertainity principle
Narrower the wave packet to begin with , the more rapidly it spreads. Because of the confinement of the packet within the region Δx_{0} the fourier analysis contains many waves of length of order of Δx_{0} , hence momenta p≅
therefore
Δv≅p/m≅
Although average velocity of the packet is equal to the group velocity , there is still a strong chance that the actual velocity will fluctuate about this average by the same amount. The distance covered by the particle is not completely determined but it may vary as much as
Δx≅tΔv≅
The spread of the wave packet may therefore be regarded as one of the manifestations of the lack of complete determination of initial velocity necesarily associated with the narrow wave packet.
Relation of stability of atom to uncertainity principle
From uncertainity principle if an electron is localized it must have on an average a high momentum and have high kinetic energy as it takes energy to localize a particle. According to uncertainity principle it takes a momentum Δp≅
W≅ (
Differentiating both the sides w.r.t. Δx and making ∂W/∂(Δx) = 0 we get
Δx≅
THis result is just the radius of first Bohr orbit although not exact but qualitative.. The limitation of the localizability of the electron is inherent in the waveparticle nature of matter. In order to have an electron in very small space , we must have very high fourier components in its wave function and therefore the possibility of very high moments. There is no way to force an electron to occpy a well defined position and still remain at rest.
SHM in short
 Simple harmonic motion is simplest form of oscillatory motion
 SHM is a kind of motion in which the restoring force is propotional to the displacement from the mean position and opposes its increase.Mathematically restoring force is
F=Kx
K=Force constant
x=displacement of the system from its mean or equilibrium position
Diffrential Equation of SHM is
d^{2}x/dt^{2} + ω^{2}x=0
 Solutions of this equation can both be sine or cosine functions .We conveniently choose
x=Acos(ωt+φ)
where A,ω and φ all are constants  Quantity A is known as amplitude of SHM which is the magnitude of maximum value of displacement on either sides from the equilibrium position
 Time period (T) of SHM the time during which oscillation repeats itself i.e, repeats its one cycle of motion and it is given by
T=2π/ω
where ω is the angular frequency  Frequency of the SHM is the number of the complete oscillation per unit time i.e, frequency is reciprocal of the time period
f=1/T
Thus angular frequncy
ω=2πf  Total energy remains constant in a SHM.So you can find the energy at any position and differentiate it to find the out the frequency
 Problem of SHM are basically to find out the timeperiod.So the concenteration should be on getting the net restoring force
 The basic approach to solve such problem is
1. Consider the system is displaced from equilibrium position
2. Now consider all the forces acting on the system in displaced position
3. find the restore force which comes out to be in the form
4.F=kx
Vector Algebra 2(quick recap)
Blog for graduate level physics: Vector Algebra 2: "In this post we'll lern Vector algebra in component form. Component of any vector is the projection of that vector along the three coordinat..."
Vector Algebra 1(quick recap)
Blog for graduate level physics: Vector Algebra 1: " Here in this post we will go through a quick recap of vector algebra keeping in mind that reader already had detail knowledge and problem s..."
Blog for graduate level physics: Force on a conductor
To read an article about force on a conductor click the link given below.
Blog for graduate level physics: Force on a conductor: "We have already learned in our previous discussion that field inside a conductor is zero and the field immidiately outside is En=n(σ/ε0) ..."
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physics expert
Blog for graduate level physics: Force on a conductor: "We have already learned in our previous discussion that field inside a conductor is zero and the field immidiately outside is En=n(σ/ε0) ..."
Hope you like it
physics expert
Force on a conductor
We have already learned in our previous discussion that field inside a conductor is zero and the field immidiately outside is
E_{n}=n(σ/ε_{0}) (1)
where n is the unit normal vector to the surface of the conductor. We also know that any charge a conductor may carry is distributed on the surface of the conductor.
In presence of an electric field this surface charge will experience a force. If we consider a small area element ΔS of the surface of the conductor then force acting on area element is given by
ΔF=(σΔS).E_{0} (2)
where σ is the surface charge density of the conductor , (σΔS) is the amount of charge on the area element ΔS and E_{0} is the field in the region where charge element (σΔS) is located.
Now there are two fields present E_{σ} and E_{0} and the resultant field both inside and outside the conductor near area element ΔS would be equal to the superposition of both the fields E_{σ} and E_{0} . Figure below shows the directions of both the fields inside and outside the conductor
E_{in}=E_{0}=E_{σ}
Since direction of E_{σ} and E_{0} are opposite to each other and outside the conductor near its surface
E_{out}=E_{0}+E_{σ}=2E_{0}
Thus , E_{0} =E/2 (3)
Equation (2) thus becomes,regardless of the of ΔF=½(σΔS).E (4)
From equation 4 , force acting per unit area of the surface of the conductor is
f=½σ.E (5)
Here is the E_{σ} electric field intensity created by charge on area element ΔS at the point very close to this area element. In this region this area element behaves as infinite uniformly charged sheet hence we have,
E_{σ}=σ/2ε_{0} (6)
Now,
E=2E_{0}=2E_{σ}=(σ/ε_{0})n=E_{n}
which is in accordance with equation 1. Hence from equation 5
f=σ^{2}/2ε_{0} = (ε_{0}E^{2}/2)n (7)
This quantity f is known as surface density of force. From equation 7 we can conclude that regardless of the sign of σ and hence direction of E , f is always directed in outward direction of the conductor.
E_{n}=n(σ/ε_{0}) (1)
where n is the unit normal vector to the surface of the conductor. We also know that any charge a conductor may carry is distributed on the surface of the conductor.
In presence of an electric field this surface charge will experience a force. If we consider a small area element ΔS of the surface of the conductor then force acting on area element is given by
ΔF=(σΔS).E_{0} (2)
where σ is the surface charge density of the conductor , (σΔS) is the amount of charge on the area element ΔS and E_{0} is the field in the region where charge element (σΔS) is located.
Now there are two fields present E_{σ} and E_{0} and the resultant field both inside and outside the conductor near area element ΔS would be equal to the superposition of both the fields E_{σ} and E_{0} . Figure below shows the directions of both the fields inside and outside the conductor
Now field E_{0} has same value both inside and outside the conductor and surface element ΔS suffers discontinuty because of the charge on the surface and this makes field E_{σ }on either side pointing away from the surfaceas shown in the figure given above. Since E=0 inside the conductor
E<sub>in=E_{0}+E_{σ}=0E_{in}=E_{0}=E_{σ}
Since direction of E_{σ} and E_{0} are opposite to each other and outside the conductor near its surface
E_{out}=E_{0}+E_{σ}=2E_{0}
Thus , E_{0} =E/2 (3)
Equation (2) thus becomes,regardless of the of ΔF=½(σΔS).E (4)
From equation 4 , force acting per unit area of the surface of the conductor is
f=½σ.E (5)
Here is the E_{σ} electric field intensity created by charge on area element ΔS at the point very close to this area element. In this region this area element behaves as infinite uniformly charged sheet hence we have,
E_{σ}=σ/2ε_{0} (6)
Now,
E=2E_{0}=2E_{σ}=(σ/ε_{0})n=E_{n}
which is in accordance with equation 1. Hence from equation 5
f=σ^{2}/2ε_{0} = (ε_{0}E^{2}/2)n (7)
This quantity f is known as surface density of force. From equation 7 we can conclude that regardless of the sign of σ and hence direction of E , f is always directed in outward direction of the conductor.
Thomson Effect
or
dV=σdT
where σ is the constant of proportinality and is known as thomson coefficent
π=Ts=T(dE/dT)
and σ =T(ds/dT)=T(d^{2}E/dT^{2})
Kinetic Energy
For full notes on Work , Energy and Power visit Physicscatalyst.com
 Kinetic energy is the energy possesed by the body by virtue of its motion
 Body moving with greater velocity would posses greater K.E in comparison of the body moving with slower velocity
 Consider a body of mass m moving under the influenece of constant force F.From newton's second law of motion
F=ma
Where a is the acceleration of the body  If due to this acceleration a,velocity of the body increases from v_{1} to v_{2} during the displacement d then from equation of motion with constant acceleration we have
v_{2}^{2} v_{1}^{2}=2ad or
a=v_{2}^{2} v_{1}^{2}/2d Using this acceleration in Newton's second law of motion
we have
F=m(v_{2}^{2} v_{1}^{2})/2d
or
Fd=m(v_{2}^{2} v_{1}^{2})/2
or
Fd=mv_{2}^{2}/2 mv_{1}^{2}/2 (7)
We know that Fd is the workdone by the force F in moving body through distance d  In equation(7),quantity on the right hand side mv^{2}/2 is called the kinetic energy of the body
Thus
K=mv^{2}/2  Finally we can define KE of the body as one half of the product of mass of the body and the square of its speed
 Thus we see that quantity (mv^{2}/2) arises purely becuase of the motion of the body
 In equation 7 quantity
K_{2}=mv_{2}^{2}/2
is the final KE of the body and
K_{1}=mv_{1}^{2}/2
is the initial KE of the body .Thus equation 7 becomes
W=K_{2}K_{1}=ΔK (9)  Where ΔK is the change in KE.Hence from equation (9) ,we see that workdone by a force on a body is equal to the change in kinetic energy of the body
 Kinetic energy like work is a scalar quantity
 Unit of KE is same as that of work i.e Joule
 If there are number of forces acting on a body then we can find the resultant force ,which is the vector sum of all the forces and then find the workdone on the body
 Again equation (9) is a generalized result relating change in KE of the object and the net workdone on it.This equation can be summerized as
K_{f}=K_{i}+W (10)
which says that kinetic energy after net workdone is equal to the KE before net work plus network done.Above statement is also known as workkinetic energy theorem of particles  Work energy theorem holds for both positive and negative workdone.if the workdone is positive then final KE increases by amount of the work and if workdone is negative then final KE decreases by the amount of workdone
Electric field due to charged conductor
We all know that electric field inside a conductor is zero and any charge a conductor may carry lies on its surface and we have discussed it already in the earlier post (read more)but to know about the field due to this charge on the surface of the conductor you can Click the link given below
Electric field due to charged conductor
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physicsExpert
Electric field due to charged conductor
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physicsExpert
Electric field due to charged conductor
In our previous post we have discussed that electric field inside a conductor is zero and any charge the conductor may carry shall be distributed on the surface of the conductor. For our discussion consider a conductor carrying charge on its surface again consider a small surface element ds over which we can consider surface charge density σ to be approximately constant.
For positive charge distributed over the surface of the conductor , electric field E would be directed at right angels to the surface pointing in outwards direction. Now E due to charge carrying conductor can be calculated using Gauss's law. For this draw a Gaussin cylendrical surface as shown below in the figure
Now S is the area of crosssection of the surface. The flux due to cylendrical surface is zero because electric field and the normal to the surface are perpandicular to each other. Since electric field inside the conductor is zero hence only contribution to the flux is due to the chare on area S lying outside the surface of the conductor. So total flux through the surface would be
From Gauss's law,
ES=q/ε_{0}=σS/ε_{0}
or,
E=σ/ε_{0}
and this is the required relation for the field of charged conductor
For positive charge distributed over the surface of the conductor , electric field E would be directed at right angels to the surface pointing in outwards direction. Now E due to charge carrying conductor can be calculated using Gauss's law. For this draw a Gaussin cylendrical surface as shown below in the figure
Now S is the area of crosssection of the surface. The flux due to cylendrical surface is zero because electric field and the normal to the surface are perpandicular to each other. Since electric field inside the conductor is zero hence only contribution to the flux is due to the chare on area S lying outside the surface of the conductor. So total flux through the surface would be
From Gauss's law,
ES=q/ε_{0}=σS/ε_{0}
or,
E=σ/ε_{0}
and this is the required relation for the field of charged conductor
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