Question

A hollow sphere of radius a has uniform surface charge density σ and is centered at the origin. It sits inside a bigger sphere, also centered at the origin, with radius b > a and uniform surface charge density −σ. Because of the spherical symmetry, the electric field will have the form () = E(r) r̂, where negative E(r) corresponds to an electric field pointing towards the origin, and positive E(r) corresponds to a field pointing away. What is E(r) for r < a? (Use any variable or symbol stated above along with the following as necessary: ε₀.)

1. E(r < a) = ？

2. What is E(r) for a < r < b?
E(a< r < b) = ？

3. What is E(r) for r > b?
E(r > b) = ？

4. Sketch E(r) as a function of r for r going from 0 to 3b. Make sure that the regions of the plot corresponding to your three answers are all roughly the same size so that they're all clearly visible. Make sure that you have labeled ticks giving the scales of both the r and E axes.

Answer 1