The electric field inside a conductor is 0 but the potential has a value. then why V=intgeral(E.dl) is zero?

Question

I'm just confused. E=0 inside a spherical shell so V=integral(E.dl) should be zero, am I correct? but this is not the case in reality. Please explain why V=integral(E.dl) is invalid. thank you.

Answer 1

Good question :)

1)ELECTRIC FIELD INSIDE A CONDUCTOR IS ZERO-

This is because , its a fact that "the extra charge on a conductor resides on its surface" WHICH MEANS THAT INSIDE A CONDUCTOR , there is no extra charge ,, there are equal protons and equal electrons. THAT IS WHY ,, THERE IS NO ELECTRIC FIELD.

2)NOW , your question is that why there is a NON ZERO POTENTIAL INSIDE. ITS A FACT THAT THE POTENTIAL AT THE SURFACE OF THE CONDUCTOR AND THE POTENTIAL INSIDE THE SURFACE IS THE SAME .DO U KNOW WHY ? ((u must know that the potential is related to the electric potential energy. its the work done by external force in bringing a charge from infinity to that point/ charge )NOW U SEE, SUPPOSE WE BRING A CHARGE FROM INFINITY TO THE SURFACE OF THE CONDUCTOR ,, U KNOW that work is done by the external force!! now that you have brought the charge , suppose you want to put it inside the conductor,, BUT !! U KNOW THAT THE ELECTRIC FIELD INSIDE THE CONDUCTOR IS ZERO ! THEREFORE, NO EXTRA WORK HAS TO BE DONE BY THE EXTERNAL FORCE! yayyy! :D that is why ,, the potential inside the conductor is non zero ,, and is equal to the potential at the surface of the conductor.



and i would like to tell you something so that you understand better .potential energy is stored in a charge when it is brought near another charge with same sign charge. because external force is positive and there is force of repulsion between the two charges. but when it is brought near another charge with the opposite charge ,,external force is negative and the force between the two is attractive. so the potential energy decreases.

Answer 2

A *static* electric field inside a conductor is 0. The potential on the conductor is constant because the charges in the conductor would move otherwise. But then the constant potential throughout the interior is a solution of the Laplace equation. But the electric field is the gradient of the potential, so it is zero there. If there are moving charges or changing magnetic fields, this argument fails and the electric filed can be non-zero. This is also easy to see since light can go through the inside of a conductor. Remember that light is an electro-magnetic wave.

Answer 3

there are two regions. inside and outside of the shell. the total potential is defined as the addition of the potentials of both the inside and outside regions. the potential inside is equal to zero, but the field outside is the integral of the efield outside. add those two together and u have the total potential.