Why E=0 inside a conductor?

Question

First

$ \rho = 0 $ inside the conductor

from $\nabla \cdot E = \rho / \epsilon_0 $ if E=0 then $ \rho $ should be 0 too

I got this concept but Why E=0 inside a conductor?

Why E=0 inside a conductor?

from em griffiths "if there were any field, those free charges would move and it wouldn't be electrostatics any more."

My question is what is the relation between conductor and electrostatics ?

Why E=0 inside a conductor?

Answer 1

$\vec E$ is not necessarily zero inside a conductor. When there is current going through a conductor then there very often is a non-zero E field.

To ensure that $\vec E=0$ requires two conditions:

1. the material must have some finite conductivity $\sigma \vec E=\vec J$

2. there must be no current $\vec J=0$

Clearly, with these two conditions we get $\vec E=0$ by substitution, but not just with condition 1.

Answer 2

You appear have the reasoning the wrong way around. It is because $\rho=0$ that $\bf E=0$ inside the conductor (the author assumes the situation is electrostatic i.e, no currents).

If you added charge to a conductor, due to repulsive forces, the charge would move to the surface of the conductor so that inside the conductor, the electric field is zero.