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### Advantages of potential formulation in electrostatics

We already know about electric field and electric potential. We also know that electrostatic field is completely characterized by vector function E(r). The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding. Now a question arises why do we need introduction of electric potential when we already have electric field for the description of electric force between charges.
Firstly, the concept of electric potential is very useful not only in physics but as well as in engineering .This is because if we know the potential we can easily calculate the work  done by field forces when a charge is displaced from point 1 to point 2 that is
${W_{12}} = q({\varphi _1} - {\varphi _2})$
where ${\varphi _1}$  and ${\varphi _2}$ are the potentials at points 1 and 2. This means that required work is equal to the decrease in the potential energy of charge q when it is displaced from point 1 to 2.
Calculation of the work of field forces with the help of above mentioned formula is not just simple but the only possible method in some cases.
Secondly in some cases of electrostatic field calculation it is often easier to first calculate the potential and then find the gradient of potential  ${\varphi}$ to calculate the value of electric field intensity E. Also for calculating ${\varphi}$ we only need to evaluate one integral but for calculation of E we must take three integrals all for x, y, and z directions since E is a vector quantity.
But we must note that for problems with high symmetry we must directly calculate E using Gauss's Theorem which is much simpler way to find electric field intensity when charge distribution is symmetrical.

### CBSE Class 10 notes on Chemical Reactions and Equations

To read full length notes on Chemical reactions and Equations for class 10 chemistry visit

### CBSE Class 9 notes on Matter in our surroundings

To read full length notes on Matter in our surroundings a class 9 chapter on chemistry visit the links given below
Matter in our surrounding part 1
Matter in our surrounding part 2

### Physics Magazine by physicscatalyst.com

Here is a copy of physics magazine published at physicscatalyst.com

### CBSE class 12 physics sample papers

Visit this
to download latest sample papers in physics for class 12 along with solutions.

### CBSE class 9 biology

Study material for class 9 biology for cbse board is now available at
http://physicscatalyst.com/class9.php
Chapters included are
1. Fundamental unit of life
2. Tissues

### Relative velocity

Before discussing relative velocity we must know that all the motion is relative. Everything moves-even things that appear to be at rest. They move relative to the Sun and stars. When we discuss the motion of something, we describe the motion relative to something else. When we say a racing car reaches a speed of 200 kilometers per hour, we mean relative to the track. Unless stated otherwise, when we discuss the speeds of things in our environment, we mean relative to the surface of Earth. Motion is relative.
Now we come to relative velocity
Before studying further I am assuming that you are familiar with the concept of frame of reference and velocity.
Observations made in different frames of reference are related to each other to know how, consider this example of two trains approaching one another, each with a speed of 90 km/h with respect to the Earth. Observers on the Earth beside the train tracks will measure 90 km/hr for the speed of each of the trains. Observers on either one of the trains (a different frame of reference) will measure a speed of 180 km/h for the train approaching them. When the velocities are along the same line, simple addition or subtraction is sufficient to obtain the relative velocity. But if they are not along the same line, we must make use of vector addition. And it is also necessary that when specifying a velocity, we specify what the reference frame is.
For further information visit
and our video link for relative velocity is

### Joint CSIR-UGC National Eligibility Test for JRF/LS for Engineering Students from 2012

“CSIR has been conducting Joint CSIR-UGC National Eligibility Test for Junior Research Fellowship and Eligibility For Lectureship in five subjects of science twice a year in the month of June and December. In order to encourage engineering graduates to pursue PhD, CSIR-NET is being extended to engineering students by introducing a sixth paper in engineering sciences which will be common to all areas of engineering disciplines from December, 2012. The eligibility criteria (educational qualification) for writing the test will be BE, B.Tech or equivalent in engineering with at least 55% marks for general/OBC and 50% marks for SC/ST, Physically and visually handicapped candidates. Students in the 4th year of the programme will also be eligible to apply. The syllabus and sample paper will be uploaded in the web by August, 2012″.

### What is entropy?

Entropy is a state function of a system, it depends only on the equilibrium state of the system. The chenge in entropy between initial and final equilibrium states is
$\Delta S=\int_{i}^{f}\frac{dQ}{T}$
where dQ is the infinitesimal heat transfer that takes place reversibly. The change in entropy for process, including irreversible one between given initial and final equilibrium state, is the same.The second law of thermodynamics may be expressed in terms of entropy, $\Delta S \geqslant 0$.
For reversible process  $\Delta S = 0$.
For irreversible process  $\Delta S > 0$.
Entropy is a measure of the disorder in a system. The second law states that the natural (irreversible) process tend to evolve to state of greater disorder, or from states of low probability to states of high probability.

### CBSE Class 9 physics notes on Newton's Laws of motion

Full length CBSE Class 9 physics notes on Newton's Laws of motion for study is now available.
To study the chapter visit the link given below
Newton's Laws of motion

### Force : Class 9 physics notes for CBSE and other boards

Class 9 physics notes on Force for CBSE and other board is now available. To read the notes visit the link

### Vector Differentiation full length notes for CSIR-NET/GATE/JAM

Full notes on vector Differentiation is now available at the website physicscatalyst.com covering following topics
1. Differentiation of vectors
2. Scalar and vector fields
3. Gradient of a scalar field
4. The operator delta
5. Divergence and curl of a vector
6. Product Rules
7. Second Derivative
For complete notes visit this link

### free physics questions with solutions for competitive exams : class 11 and class 12

HI
I am pleased to announce the beginning of our all new and free online learning program in physics where you can find physics questions along with their answers and solutions. For this you just have to register onto our website by following this
So what are you waiting for register with our site and start preparing physics for your exams.
physicsexpert

### CBSE class 10 Reflection of light full length notes

Class 9 physics notes on chapter Reflection of light is now available at the following link
CLASS 10 REFLECTION OF LIGHT NOTES (FULL LENGTH)

### CBSE class 9 motion full length notes

Class 9 physics notes on chapter motion is now available at the following link
CLASS 9 MOTION NOTES (FULL LENGTH)

### H.C Verma Concepts of physics OR NCERT physics books

Many times i have had users ask me a question which book to opt between H.C Verma Concepts of physics and NCERT physics books. My answer is you can keep both the books set for your preparation as NCERT is nice book to learn a good concepts and is according to the exam level of class 11 and class 12. But what i think about  HC verma is that it is the best book for problems ,go for solved as well asboth unsolved questions in HC verma and do practice them without looking at the solutions. MCQ and conceptual problems given in the book are good. So the book is also good for objective purpose but first do subjective questions to get a grip over the concepts you have learned. You can also first solve the questions given in the NCERT book as they are bit easy in comparison to the questions given  in the HC Verma book. For further reference you can consult books like resnik halliday to get and in depth knowledge of  theory.

### CBSE Class 11 physics syllabus

Unit I: Physical World and Measurement (Periods 10)
Physics: Scope and excitement; nature of physical laws; Physics, technology and society.
Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived
units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in
measurement; significant figures.
Dimensions of physical quantities, dimensional analysis and its applications.
Unit II: Kinematics (Periods 30)
Frame of reference, Motion in a straight line: Position-time graph, speed and velocity. Uniform and
non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocitytime and position-time graphs, relations for uniformly accelerated motion (graphical treatment).
Elementary concepts of differentiation and integration for describing motion. Scalar and vector
quantities: Position and displacement vectors, general vectors and notation, equality of vectors, multiplication
of vectors by a real number; addition and subtraction of vectors. Relative velocity.
Unit vectors. Resolution of a vector in a plane – rectangular components.
Scalar and Vector products of Vectors. Motion in a plane. Cases of uniform velocity and uniform
acceleration – projectile motion. Uniform circular motion.
Unit III: Laws of Motion (Periods 16)
Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second
law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its
applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on
Unit IV: Work, Energy and Power (Periods 16)
Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.
Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical
energy (kinetic and potential energies); non-conservative forces; motion in a vertical circle, elastic and
inelastic collisions in one and two dimensions.
Unit V: Motion of System of Particles and Rigid Body (Periods 18)
Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre
of mass of a rigid body; centre of mass of uniform rod.
Moment of a force, torque, angular momentum, conservation of angular momentum with some
examples.4
Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear
and rotational motions; moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects
(no derivation). Statement of parallel and perpendicular axes theorems and their applications.
Unit VI: Gravitation (Periods 14)
Kepler’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its
variation with altitude and depth.
Gravitational potential energy; gravitational potential. Escape velocity, orbital velocity of a satellite.
Geostationary satellites.
Unit VII: Properties of Bulk Matter (Periods 28)
Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear,
modulus of rigidity, poisson’s ratio; elastic energy.
Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes).
Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Critical
velocity, Bernoulli’s theorem and its applications.
Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension
ideas to drops, bubbles and capillary rise.
Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous
expansion. Specific heat capacity: Cp , Cv
– calorimetry; change of state – latent heat.
Heat transfer – conduction and thermal conductivity, convection and radiation. Qualitative ideas of
Black Body Radiation, Wein’s displacement law, and Green House effect.
Newton’s law of cooling and Stefan’s law.
Unit VIII: Thermodynamics (Periods 12)
Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and
internal energy. First law of thermodynamics. Isothermal and adiabatic processes.
Second law of thermodynamics: Reversible and irreversible processes. Heat engines and refrigerators.
Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods 8)
Equation of state of a perfect gas, work done on compressing a gas.
Kinetic theory of gases: Assumptions, concept of pressure. Kinetic energy and temperature; rms
speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application
to specific heat capacities of gases; concept of mean free path, Avogadro’s number.
Unit X: Oscillations and Waves (Periods 28)
Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple
harmonic motion (SHM) and its equation; phase; oscillations of a spring – restoring force and force constant;
energy in SHM – kinetic and potential energies; simple pendulum – derivation of expression for its time
period; free, forced and damped oscillations (qualitative ideas only), resonance.
Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a
progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and
organ pipes, fundamental mode and harmonics. Beats. Doppler effect.5
PRACTICALS
Total Periods 60
Section A
Experiments
1. To measure diameter of a small spherical/cylindrical body using Vernier callipers.
2. To measure internal diameter and depth of a given beaker/calorimeter using Vernier callipers and
hence find its volume.
3. To measure diameter of a given wire using screw gauge.
4. To measure thickness of a given sheet using screw gauge.
5. To measure volume of an irregular lamina using screw gauge.
6. To determine radius of curvature of a given spherical surface by a spherometer.
7. To determine the mass of two different objects using a beam balance.
8. To find the weight of a given body using parallelogram law of vectors.
9. Using a simple pendulum, plot L-T and L-T
2
graphs. Hence find the effective length of a second’s
pendulum using appropriate graph.
10. To study the relationship between force of limiting friction and normal reaction and to find the
coefficient of friction between a block and a horizontal surface.
11. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of
the earth and study its relationship with the angle of inclination (?) by plotting graph between force
and sin ?.
Activities
1. To make a paper scale of given least count, e.g. 0.2 cm, 0.5 cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in the range of a jet of water with the angle of projection.
6. To study the conservation of energy of a ball rolling down on inclined plane (using a double
inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of
amplitude and time.6
Section B
Experiments
1. To determine Young’s modulus of elasticity of the material of a given wire.
2. To find the force constant of a helical spring by plotting a graph between load and extension.
3. To study the variation in volume with pressure for a sample of air at constant temperature by
plotting graphs between P and V, and between P and 1/V.
4. To determine the surface tension of water by capillary rise method.
5. To determine the coefficient of viscosity of a given viscous liquid by measuring the terminal velocity
of a given spherical body.
6. To study the relationship between the temperature of a hot body and time by plotting a cooling
curve.
7. To determine specific heat capacity of a given (i) solid (ii) liquid, by method of mixtures.
8. (i) To study the relation between frequency and length of a given wire under constant tension
using sonometer.
(ii) To study the relation between the length of a given wire and tension for constant frequency
using sonometer.
9. To find the speed of sound in air at room temperature using a resonance tube by two resonance
positions.
Activities
1. To observe change of state and plot a cooling curve for molten wax.
2. To observe and explain the effect of heating on a bi-metallic strip.
3. To note the change in level of liquid in a container on heating and interpret the observations.
4. To study the effect of detergent on surface tension of water by observing capillary rise.
5. To study the factors affecting the rate of loss of heat of a liquid.
6. To study the effect of load on depression of a suitably clamped meter scale loaded at (i) at its end
(ii) in the middle.

### CBSE Class 12 physics syllabus

Unit I: Electrostatics (Periods 25)
Electric charges and their conservation. Coulomb’s law – force between two point charges, forces
between multiple charges; superposition principle and continuous charge distribution.
Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to
a dipole; torque on a dipole in a uniform electric field.
Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long
straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of
charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipoles in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a
capacitor, Van de Graaff generator.
Unit II: Current Electricity (Periods 22)
Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their
relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity.
Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors;
temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff ’s laws and simple applications. Wheatstone bridge, metre bridge.
Potentiometer – principle and applications to measure potential difference, and for comparing emf of
two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)
Concept of magnetic field, Oersted’s experiment. Biot – Savart law and its application to current
carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force
on a moving charge in uniform magnetic and electric fields. Cyclotron.
Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel currentcarrying conductors – definition of ampere. Torque experienced by a current loop in a magnetic field;
moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a
revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and
perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferro – magnetic substances, with examples.
Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents
(Periods 20)
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self
and mutual inductance.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer.
Unit V: Electromagnetic Waves (Periods 4)
Need for displacement current.
Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of
electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma
rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its
applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula.
Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror.
Refraction and dispersion of light through a prism.
Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects
(myopia and hypermetropia) using lenses.
Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: Wavefront and Huygens’ principle, reflection and refraction of plane wave at a plane
surface using wavefronts.
Proof of laws of reflection and refraction using Huygens’ principle.
Interference, Young’s double hole experiment and expression for fringe width, coherent sources and
sustained interference of light.
Diffraction due to a single slit, width of central maximum.
Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light;
Brewster’s law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods
Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle
nature of light.
Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment
(experimental details should be omitted; only conclusion should be explained.)
Unit VIII: Atoms and Nuclei (Periods 18)
Alpha – particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels,
hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.
Radioactivity – alpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear
fission and fusion.
Unit IX: Electronic Devices (Periods 18)
Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors;
semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics
of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor,9
transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration)
and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and
digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere,
sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated
wave.
Practicals
Total Periods 60
Section A
Experiments
1. To find resistance of a given wire using metre bridge and hence determine the specific resistance
of its material.
2. To determine resistance per cm of a given wire by plotting a graph of potential difference versus
current.
3. To verify the laws of combination (series/parallel) of resistances using a metre bridge.
4. To compare the emf ’s of two given primary cells using potentiometer.
5. To determine the internal resistance of given primary cell using potentiometer.
6. To determine resistance of a galvanometer by half-deflection method and to find its figure of
merit.
7. To convert the given galvanometer (of known resistance of figure of merit) into an ammeter and
voltmeter of desired range and to verify the same.
8. To find the frequency of the ac mains with a sonometer.
Activities
1. To measure the resistance and impedance of an inductor with or without iron core.
2. To measure resistance, voltage (ac/dc), current (ac) and check continuity of a given circuit using
multimeter.
3. To assemble a household circuit comprising three bulbs, three (on/off) switches, a fuse and a
power source.
4. To assemble the components of a given electrical circuit.
5. To study the variation in potential drop with length of a wire for a steady current.
6. To draw the diagram of a given open circuit comprising at least a battery, resistor/rheostat, key,
ammeter and voltmeter. Mark the components that are not connected in proper order and correct
the circuit and also the circuit diagram.
Section B
Experiments
1. To find the value of v for different values of u in case of a concave mirror and to find the focal
length.
2. To find the focal length of a convex mirror, using a convex lens.
3. To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and
1/v.
4. To find the focal length of a concave lens, using a convex lens.
5. To determine angle of minimum deviation for a given prism by plotting a graph between the angle
of incidence and the angle of deviation.
6. To determine refractive index of a glass slab using a travelling microscope.
7. To find refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
8. To draw the I-V characteristics curves of a p-n junction in forward bias and reverse bias.
9. To draw the characteristics curve of a zener diode and to determine its reverse break down
voltage.
10. To study the characteristics of a common-emitter npn or pnp transistor and to find out the values
of current and voltage gains.
Activities
1. To identify a diode, an LED, a transistor, and IC, a resistor and a capacitor from mixed collection
of such items.
2. Use of multimeter to (i) identify base of transistor, (ii) distinguish between npn and pnp type
transistors, (iii) see the unidirectional flow of current in case of a diode and an LED, (iv) check
whether a given electronic component (e.g. diode, transistor or IC) is in working order.
3. To study effect of intensity of light (by varying distance of the source) on an LDR.
4. To observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab.
5. To observe polarization of light using two polaroids.
6. To observe diffraction of light due to a thin slit.
7. To study the nature and size of the image formed by (i) convex lens (ii) concave mirror, on a
screen by using a candle and a screen (for different distances of the candle from the lens/mirror).
8. To obtain a lens combination with the specified focal length by using two lenses from the given set
of lenses.