# Metal sphere and electric field

1. Feb 21, 2006

### cherrios

This problem is somewhat similar to the one I had posted yesterday.

There is a metal spehre, radius=x, that it surrounded by a conducting shell (also spherical) that has an inner radius=y and outer radius=Z

1)Find electric field between the outer surface of the metal sphere and the inner radius of the conducting shell.

Would I need to take a Gaussian surface between the outer surface of the metal sphere and inner radius of the conducting shell? And also, how would I find the surface charge density on the inner and outer surfaces of the conducting shell?

2. Feb 21, 2006

### topsquark

We need to know where the charge is in the system.

Two tips in general about conductors: The electric field inside a conductor is zero. There are no charges inside of a conductor, they all migrate to the surfaces.

-Dan

3. Feb 21, 2006

### cherrios

Sorry, the total charge is 4 micro Coloumbs--> 1 micro Coloumb on the inner sphere, and the rest is distributed in the shell

4. Feb 21, 2006

### topsquark

Okay, so inside the conductor, what is the electric field? (Zero by definition!) What does Gauss' Law tell you about the amount of charge inside your Gaussian surface? Since the conductor was initially neutral (I'm assuming) what does that mean for the outer surface of the conductor?

-Dan

5. Feb 22, 2006

### cherrios

I think that the outer surface would probably have no charge then?

6. Feb 22, 2006

### topsquark

Okay, the metal sphere has a charge of 4 microCoulomb on it (positive I'm assuming). So, you want the charge on the surfaces of the spherical conductor surrounding it.

Consider a Gaussian surface inside your conductor. Since the electric field inside a conductor is zero, Gauss' Law predicts that the total charge inside the Gaussian surface is zero. But we know that +4 microCoulomb are on the metal sphere, so the only way this can happen is if -4 microCoulomb is in the conductor volume of your Gaussian surface. But free charges don't stay inside conductors...they flow to the surfaces. So you now know that there is -4 microCoulomb of charge on the inside surface of the conductor. This charge will be spread evenly over the surface area.

So if your initially neutral conductor has -4 microCoulomb on its inner surface, what is the charge on the outer surface?

-Dan