# The electric field inside a shell with a charge at the center?

1. Apr 17, 2010

### wil3

Hello. I am preparing for the AP Physics C E&M exam, and I am trying to understand the solution to 2004-1

The problem provides an infinite line of uniform charge per unit length enclosed within an infinite hollow conducting cylinder with a fixed radius and no net charge. The line of charge within the tube is off center.

In one of the parts of the question, it asks to draw all field lines an induced charges. I correctly drew the induced dipoles within the metal shell, but the answer key says that there is no field between these dipoles (ie, field is zero everywhere within the conductor)

How is this possible? The best qualitative explanation I can come up with is that at any point within the solid conductor, the field due to the dipole is exactly canceled out by the field due to the line of charge (ie, even though the dipole is closer, the charge is less because it has been mitigated by being evenly distributed over the surface. I'm guessing that the loss of charge is exactly proportional to the decrease in radius to the charge, so that the dipole vector is equal and opposite the field vector from just the line)

Can someone give a qualitative or quantitative explanation of what is happening here?

2. Apr 17, 2010

### quantum13

Logically,

If there were a net electric field in a conductor then it would be moving the electrons inside, and if it moves the electrons inside, there is current. But an isolated conductor does not carry a perpetual current so there cannot be an electric field inside.

The electrons are moved into such a distribution that all the electric field vectors cancel, which is something like what you described.

I'm guessing you self-studied the material because I think in classes people just memorize that the electric field in a conductor is zero (although I don't know, I'm self-teaching this stuff too).