# Is electric field inside a conducting metal (hollow) body zero even if the the charge on it is negative?

Consider any conducting metal hollow body(NOT A SPHERE PLEASE) and allow negative charges to reside on it.The electric field due to the charges should be outward right?So will the field inside the conductor zero?(Appreciate if the answer contains a visual(Diagram))

• Any reason why you don't want the hollow body to be a sphere? – Kelvin Onggadinata Oct 3 '17 at 4:40
• The reason I didn't wanted it to be a sphere was just to get the answer in a more generalised manner(So that there are no chances of symmetry) – Divyanshu Oct 3 '17 at 4:54

Yes, electric field in a hollow inside a conducting metal body is zero. It doesn't matter if the hollow is sphere or not, if the body is charged or not and if it is charged, if the charge is positive or negative.

Here is a proof (not rigorous though).

1. Let's temporarily fill the hollow with metal. Now we have just a charged metal body. There could be no electric field inside the body. Because if there was, there would be an electric current.

2. As there is no electric field - the material is not charged. This is because if some charges are present in the area, the electric field can't be constant in this area: electric field lines must either originate or end up in this region. Or shorter: charge density $\rho \sim div(\vec{E})$; $\vec{E} = 0 => div(\vec{E}) = 0 => \rho = 0$

3. We have some equilibrium state now: all the electric charges are distributed in a way that existing electric field would not move them anywhere. Now let's remove the metal we have temporarily put into the hollow on step one. Note, that we are moving no charges while doing so. We are removing some material with zero charge from the area with no electric field. This wouldn't affect the charges distribution picture.

If step 3 is not looking good for you, you can do the following. Before removing the metal fix all the charges in the rest of the system so they wouldn't move. Now you remove the metal. Charges distribution still the same => electric field is still the same. Now you can let go all the charges, but they wouldn't move, because the existing electric field has not changed and these charges wouldn't move anywhere in the very same electric field before you removed the metal from the hollow.

So, the electric field remains zero in the hollow (and anywhere inside the conductor). Sorry for no pictures...

Say,it has a field inside it's body.Then,due to its effect,the charges will also flow on the surface the conductor.This flow will continue until the field is neutralised by the flow of the charges.After it is neutralised,there can not be any more field inside its body.