Modification to metal sphere problem

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

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?

 

[gulsen]

Assuming that you have no induction and uniform chage density, the outer shell will not contribute to the electric field, since it has no charge between it and inner shell. You simply have $$q_{in} = 1\mu C$$, and by Gauss's law for a spherical shell
$$\int \vec{E}.d\vec{A} = \int EdA = E \int dA = E(4 \pi r^2) = \frac{q_{in}}{\epsilon_0}$$, which will yield E(r).

 

[kyle8921]

To find the electric field between the outer surface of the metal sphere and the inner radius of the conducting shell, you can use Gauss's law. The electric field will be constant and will have a magnitude of 4 micro Coloumbs divided by the area of the Gaussian surface.

To find the surface charge density on the inner and outer surfaces of the conducting shell, you can use the fact that the electric field inside a conductor is zero. This means that the electric field on the inner surface of the conducting shell must be equal and opposite to the electric field on the outer surface of the metal sphere. You can then use the electric field equation to solve for the surface charge density on both surfaces.