Question

if electric field iside a conductor is 0 ,so there must not be an electric force experienced by a charge inside it so work done =0 if a charge is inside the conductor then how is that the potential inside is constant and not zero as the potential is work done per unit chage????

Answer 1

Hi Amitshukla,
There is no electric field and a constant non-zero potential inside a conductor indeed in case of electrostatic equilibrium. Just an example. Imagine a solid metal sphere with say net negative charge. You go with an electron in your pocket towards this sphere from the infinity. Do you have to do some work? Yes, because negative charge on the sphere and your electron repel each other. The repelling force goes more and more as you come closer to the sphere, so the work you've made also increases. When you are ready to touch the sphere with your electron, the work reaches its maximum, and it is not zero. If we divide this work by the charge (1e in our case), then we have a potential of the sphere. It is evidently does not equal to zero. As long as E field inside a conductor is 0, so there should not be any changes in the potential anymore.
BTW, the potential should not be zero for work to be zero. You just have to stay on the same potential of any magnitude.
Hope it helps!

Answer 2

There's no electric field inside a conductor if the middle of the conductor is source free (Gauss' Law). If you put a charged particle into the middle, then the middle is no longer source free. Guass' Law says that the net electric flux is proportional to the charge enclosed.

\[\int\limits_{a}^{b}EdA=\frac{ \rho }{ \epsilon }\]

If the charged particle is allowed to move, then it will move to the skin of the conductor, and the internal region will be source free again, meaning that there's no internal electric field.

Answer 3

Simply put, potential is zero at infinity. I move the charge from infinity, closer and closer to the conductor carrying charge, and I have to do some work (it could either be positive or negative) to bring the charge closer to the conductor.

Inside the conductor, the E field is zero (This is an entirely separate question/proof). So basically I can move in any fashion I want and I wouldn't be doing any ADDITIONAL work. So the potential remains constant.

Remember, you are traveling from infinity to the point in question. Work done is the cumulative work you do as you go from infinity to the point in question. You can't just look inside of the conductor.