Question

Mathematical proof that electric field is zero inside a conductor

Answer 1

Originally Answered: Why is the electric field zero inside the conductor?

Say you have a conductor.

In the normal case, when there is no external field, there is no field inside the conductor, so field is zero.

Let’s talk of the other case. Initially the conductor is in a position like shown below in absence of external field (Blue dots are electrons. Of course, I have not shown all electrons. The idea is that charge is uniformly distributed).



Suppose you switch on an Electric Field, maybe you bring a very large charged metallic sheet.

Now, you might say, “Aha! there’s the field inside conductor”. But you’re forgetting a thing. It’s a conductor. There are free charges (free to move throughout the bulk of conductor). So, in presence of external field, these charges experience a force.

And here's the most crucial bit:

“These charges rearrange themselves until they no longer experience a force.”