Undergrad Why is the E-field inside a solid conducting sphere zero?

[OmegaKV]

The common explanation is this: If the conductor has a net charge, then the charges repel each other until they arrange themselves symmetrically around the outside of the sphere, and if you do the math the electric field will cancel out everywhere inside the conducting sphere.

Alright, but what if the charge is placed on a point outside of the sphere instead of on the sphere? If you keep the charge separate from the conducting sphere, then the charges won't be able to arrange themselves symmetrically around the sphere to make the electric field inside the conductor cancel out. What keeps the electric field inside the conductor zero in this case?

 

[Doc Al]

If you keep the charge separate from the conducting sphere, then the charges won't be able to arrange themselves symmetrically around the sphere to make the electric field inside the conductor cancel out.

The charges within the conducting sphere will arrange themselves so that they cancel any imposed field from the charges outside the sphere. That rearrangement will not be symmetric.

 

[OmegaKV]

The charges within the conducting sphere will arrange themselves so that they cancel any imposed field from the charges outside the sphere. That rearrangement will not be symmetric.

Interesting, I hadn't previously considered that there are charges on the conductor when it is electrically neutral.

 

[Doc Al]

I hadn't previously considered that there are charges on the conductor when it is electrically neutral.

Sure. What makes a conductor a conductor is the presence of mobile charge carriers (such as electrons) that can move easily in response to an imposed field. In the electrostatic case, the charges will move until the imposed field is canceled.

 

[vanhees71]

It's a mathematical theorem of potential theory. In the case of the sphere you can find the Green's function analytically, using the method of "image charges". You'll find that in the case that charges are present only outside of the sphere the field inside is 0.