Question

1. A very long, uniformly charged cylinder has radius R and charge density \rho. Determine the electric field of this cylinder inside (r<R) and outside (r>R)

2. A large, flat, nonconducting surface carries a uniform surface charge density σ. A small circular hole of radius R has been cut in the middle of the sheet. Determine the electric field at a distance z directly above the center of the hole.

3. You have a solid, nonconducting sphere that is inside of, and concentric with, a hollow conducting sphere. The inner sphere has a radius R1 and uniform volume charge density of \rho; the outer sphere has a radius R2 and uniform surface charge density of σ, and there is empty space between them. Note that R1<R2. Find the electric field in three regions:

(a) Inside the inner sphere (r<R1),

(b) between them (R1<r<R2), and

(c) outside the outer sphere (r>R2).

Answer 1