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

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 cross-section 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/ε0=σS/ε0
or,
E=σ/ε0
and this is the required relation for the field of charged conductor

Motion of Charged Particle in The Magnetic Field

  • As we have mentioned earlier magnetic force F=(vXB) does not do any work on the particle as it is perpendicular to the velocity.
  • Hence magnetic force does not cause any change in kinetic energy or speed of the particle.
  • Let us consider there is a uniform magnetic field B perpendicular to the plane of paper and directed in downward direction and is indicated by the symbol C in figure shown below.





  • Now a charge particle +q is projected with a velocity v to the magnetic field at point O with velocity v directed perpendicular to the magnetic field.
  • Magnetic force acting on the particle is

    F=q(v X B) = qvBsinθ
    Since v is perpendicular to B i.e., angle between v and B is θ=90 Thus charged particle at point O is acted upon by the force of magnitude
    F=qvB
    and the direction of force would be perpendicular to both v and B
  • Since the force f is perpendicular to the velocity, it would not change the magnitude of the velocity and the peffect of this force is only to change the direction of the velocity.
  • Thus under the action of the magnetic force of the particle will more along the circle perpendicular to the field.
  • Therefore the charged particle describe an anticlockwise circular path with constant speed v and here magnetic force work as centripetal force. Thus

    F=qvB=mv2/r
    where radius of the circular path traversed by the particle in the magnetic in field B is given as
    r=mv/qB                   ---(5)
    thus radius of the path is proportional to the momentum mv pof the charged particle.
  • 2πr is the distance traveled by the particle in one revolution and the period T of the complete revolution is

    T=2 πr /v
    From equation(5)
    r/v=m/qB
    time period T is
    T=2πm/qB                   (6)
    and the frequency of the particle is f=1/T=qB/2πm                   (7)
  • From equation (6) and (7) we see that both time period and frequency does not dependent on the velocity of the moving charged particle.
  • Increasing the speed of the charged particle would result in the increace in the radius of the circle. So that time taken to complete one revolution would remains same.
  • If the moving charged particle exerts the magnetic field in such a that velocity v of particle makes an angle θ with the magnetic field then we can resolve the velocity in two components

    vparallel : Compenents of the velocity parallel to field
    vperpendicular :component of velocity perpendicular to magnetic field B
  • The component vpar would remain unchanged as magnetic force is perpendicular to it.
  • In the plane perpendicular to the field the particle travels in a helical path. Radius of the circular path of the helex is

    r=mvperpendicular/qB=mvsinθ/qB                   (8)
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How conductors behave in the presence of electrost...

I have written a detail article about behaviour of conductors in the presence of electric field. Please visit the link given below to read a detailed discussion about the topic.
Blog for graduate level physics: How conductors behave in the presence of electrost...: "We know that conductors like copper , silver, aluminium etc. , have very large number of free and movable charge carriers , usually one free..."
Thanks
PhysicsExpert

How conductors behave in the presence of electrostatic field

We know that conductors like copper , silver, aluminium etc. , have very large number of free and movable charge carriers , usually one free electron per atom. These free electrons are not bound to its atom and moves freely in the space between the atoms. These free electrons can move under the action of electric field present inside the conductor.
Consider an arbitrary shaped conductor placed inside an electric field such that the field in the conductor is directed from left to right. As a result of this electric field positive charge in the conductor moves from left to right and negative charge moves from right to left. As a result there is a surplus negative charge on the left side of the conductor and a surplus positive charge on the right side of the conductor. This induced surplus chare on both the sides of the conductor acts as a source of an induced electric field which is directed from right to left i.e., in the direction opposite to the initial electric field.
Now with the increase in the amount of induced electric charges, magnitude of induced electric field also increases which cancels out the original electric field having direction opposite to it. This results in a progressive decrease in total field inside the conductor. In the end induced electric field cancels out all the initial electric field thus reaching an electrostatic equilibrium where there is zero electric field at each and every point inside the conductor. Hence we can conclude thet,
E=0 inside the conductor
Now if we apply Gauss's law to any arbitrary surface inside the conductor then total charge enclosed by the gaussian surface equals zero as vector E=0 at all points inside the gaussian surface. From this we conclude that
Al the excess charge (if any) is distributed on the surface of the conductor
We have established the fact that there is no E inside the conductor so tangential component of E is zero on the surface of the conductor hence the potential difference between any two points on the surface of the conductor would also be zero. This indicates that the surface of conductor in electrostatics is equipotential one. Since there is no E inside the conductor so all the points in the conductor are at the same potential.
This is almost all I intended to write in this topic however if you have any doubts then let me know and also you can tell me about the topic you want me to write next in the blog.

Newton's First Law of motion

Hi all

What comes to your mind when you think about Newton's first law of motion . Now a days it has become an obvious statement but it was not the case when the law has been formulated. Statement of Newton's first Law of motion is

" Every body continues to be in state of rest or uniform motion untill acted upon by a net external force."

Equilibrium of the bodies is the essence of the forst law of motion.

Why we have used the word net force it is because there might be more then one forces acting on the body and net force on the body is the vector sum of all the forces acting on the body. Newton's first law of motion only gives the qualitative defination of the force that is it tells us that force is only the influence behind the moving objects but it does not tell anything about what is required to keep objects moving when they are set to motion by the application of force. In out daily life we see that bodies set to motion eventualy came to rest for example book placed on a horizontal surface is pushed , it started to move and then come to rest. What does first law of motion has to explain about this effect. What would we have to do to keep the book moving ? Can first law of motion has anything to say about it. Think about it if you find any more point to discuss let me know I'll be happy to discuss

Physics Expert
For complete notes on Newton's Laws of motion visit Newton's Laws of motion

Electrostatics

You all know physicsgoeasy is my blog and i had already given a good amount of notes on basic electrostatics in this blog so I did not intend to write further on basic electrostatics topics. For detailed basic notes on electristatics you can visit my website physicscstalyst.com and links to my blog postes of electrostatic related material are given below.
Learn Physics for IITJEE , AIEEE , PMT and CBSE Board Examination: Electricity Index: "Electric Charge and Coulumb Law Electric Field Charge Density And Conductor Electricty Test Series -1 Electric Potential Electric Flux and G..."
However I will discuss complicated and higher level electrostatic related topics in this blog.

Crystals

Many materials like carbon can exist in various forms for example it can exist as diamond in solid form and graphite is also one form of carbon and clearly dimond and graphite have different mechanical, thermal, optical and electrical properties. These properties of different forms of carbon can be understood in terms of carbon atoms in the solid structure.
The atoms having no regular arrangement of atoms in their structure are called amorphous solids and those having regular or orderly arrangement of atoms in their structure are called crystalline solids. Graphite is an amorphous solid and diamind is a crystalline one.
Crystalline solids or crystals have periodic arrangements constructed by infinite repetion of identical structural units in space. In simple crystals structural unit is a single atom but it could be group of atoms or molecules attached to every lattice point. Structure of all crystals is described in terms of lattice.
One of simple type of crystal structures is Sodium chloride is a crystal structure having face centered cubic crystal lattice. Its basis consists of one Na and one Cl atom separated by half the body digonal of a unit cube. Each atom in sodium chloride cryatal has six nearest atoms of opposite kind. Space lattice of diamond is a face centered cubic crystal. The conventional unit cube of a diamond crystal contains 8 atoms and the basis of diamond contains only one atom that is carbon atom. Thus each point of fcc lattice have two identical atoms attached as its primitive basis.
This post is purely an informational one and is beyond your course you intend to study for your board and competetive exams.

Properties of light

1. Speed of light is greatest in the vacuum and it approximate value is 3 x 108. This value of speed of light is same for all wavelengths.
2. light has got dual nature i.e., sometimes it acts as particles and sometimes a s waves depending on the situation for example Einstein photoelectric effect experiment establishes particle properties of waves and experiments like interference and diffraction of waves establishes wave nature of light.
3. Light waves does not require any medium for its propagation.
4. When light waves travels from one medium to another it's frequency remains unchanged however its wavelength and speed do changes with the change of medium.
5. Frequency of light determines its frequency.
6. Light follows the path along which it takes less time to travel from one place to another i.e., it travels in accordance to Fermat's principle.
7. All bodies which emits light are known as sources of light and light sources can be of any shape or size.
8. When a source of light possess its own it is termed as luminious for example sun and if it does not have its own light but it visible because of reflected light from it then it is known as non luminous source of light for example human body etc..

Thermal interactions between macroscopic systems

To begin with we first define the macroscopic state or macrostate of a system. Macrostates of a system can be defined by specifying the external parameters of the system (for example volume of any system) and any other conditions or constraints imposed on the system for example consider an isolated system , macrostates of this system can be specified by specifying the parameters of the system like volume of the system and total energy of the system which is constant.
For discussing thermal interactions between two systems let us consider two macroscopic systems S and S' which are allowed to interact with each other in a way that they both can only exchange energy but we must keep in mind that total energy of combined system S+S' remains constant. For pure thermal interactions to take place between two systems external parameters of the system remains constant so that energy levels of the system does not change. Because of thermal interactions between two systems energy transfer takes place between two systems and the mean energy transfer takes place between two systems i.e., from one system to another. This mean energy transfer between two systems as a result of pure thermal interactions between these two systems is known as HEAT.
Consider change in mean energy of system S is known as heat absorbed by the system. We all know that heat transfer between two systems can be negative as well as positive. The quantity we say -Q is called heat given off by the system. Since combined energy of both the systems is constant from this statement we can conclude that
Q+Q'=0 or, Q=-Q'
From above expression we can draw a conclusion that heat absorbed by one system is equal to heat given off by another system. Thus due to thermal interactions between two systems S and S' transfer of heat takes place from one system to another and remember that in case of pure thermal interactions external parameters of the system always remains constant.

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Torque


  • Torque of a force about any point is equal to the product of the force and perpandicular distance of the line of action of force from the point.
    τ= Force x perpandicular distance from line of action from point = Frsinθ =(Fsinθ)r
    or,
    τ= (component of force perpandicular to position vector) x (position vector)
  • Unite of torque (a) MKS system --- N-m (b) CGS system --- dyne-cm.
  • Dimension of torque is ML2T-2
  • In vector form τ=F x r
  • Torque is a vector quantity having direction perpandicular to the plane of force and position vector and its direction is given by right hand rule.
  • If the torque acting on a body tends to rotate in anticlockwise direction then torque is positive and if it tends to rotate the body in clockwise direction then the is negative.
  • If the body s acted upon by more then one forces then total torque on the body is the vector sum of each torque.
  • τ= dJ/dt , where J is the angular momentum of the body.
  • The more is the value of r , more will be the torque and it would be easier to rotate the object.
  • Work done by the torque is ∫>τdθ = Torque x angular displacement. here limits of integration goes from θ1 to θ2

Superconductors and Superconductivity

Phenomenon of superconductivity was first observed by Kamerlingh Onnes in Leiden in 1911 ,3 years after he first liquified helium gas. He observed that electrical resistivity of such as mercury, tin, lead completely disappear i.e., suddenly dropped to zero in a small range of temperature at a critical temperature TC which is the characterstics of the material. This heppens when the specimen is cooled down to sufficiently low temperature about few degrees of Kelvin. At critical temperature TC specimen undergoes a phase transition from normal electrical resistivity state to superconducting state. Magnetic properties exhibited by superconductors are as interesting as its electrical properties. Now imagine what happened when a specimen known to exhibit superconductivity is placed in a magnetic field and s then cooled through the transition temperature for superconductivity. In this case magnetic field originally present in the specimen is ejected out from the specimen and this is nothing but the Meissner Effect. Information i had given here in this page is nothing but a mere definition of superconductivity phenomenon. It is a very vast topic and has a lot in it. For more information on superconductors you can visit

Ampere's Law

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  • Ampere's law in magnetism is similar to the Gauss's law in electrostatics.
  • With the help of this law we can find the magnetic fiels caused by symmetric current configurations.
  • Statement:-"The line integral B.dl around any closed path equals μ0I ,where I is the net steady curent passing through any surface bounded by a closed path. Mathematically
    B.dl = μ0I
    where integral is evaluated along a closed path.
  • Without going into the details of how to prove the law I will give you some handy things to remember while solving problems using Ampere's law.
    1. If B is everywhere tangent to the path of integration and has same magnitude B at every point on the amperian loop then the line integral becomes equal to B times the circumfrance of the path.
    2. If B is everywhere perpandicular to the amperian loop or over some portion of the loop then that portion of the loop does not make any contribution to the line integral because B.dl = Bdlcos90 = 0
    3. In the integral ∫B.dl B is the the total magnetic field at each point in the path i.e., field at any point P on the loop is due to both current sources inside and outside the Amperian loop . However the integral ∫B.dl is always zero for currents outside the Amperian loop.
    4. Things should be keept in mind before choosing the Amperian loop that points at which field is to be determined must always lie on the Amperian loop and the path or the loop must have enough symmetry so that line integral can easily be evaluated.

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