## 2011E1.
A nonconducting, thin, spherical shell has a uniform surface charge density σ on its outside surface and no charge anywhere else inside.
(a) Use Gauss's law to prove that the electric field inside the shell is zero everywhere. Describe the Gaussian surface that you use.
(b) The charges are now redistributed so that the surface charge density is no longer uniform. Is the electric field still zero everywhere inside the shell?
\\_\\_\\_ Yes \\_\\_\\_ No \\_\\_\\_ It cannot be determined from the information given.
Justify your answer.
Now consider a small conducting sphere with charge +Q whose center is at corner A of a cubical surface, as shown below.
(c) For which faces of the surface, if any, is the electric flux through that face equal to zero?
\\_\\_\\_ ABCD \\_\\_\\_ CDEF \\_\\_\\_EFGH\\_\\_\\_ ABGH \\_\\_\\_BCFG\\_\\_\\_ ADEH Explain your reasoning.
(d) At which corner(s) of the surface does the electric field have the least magnitude?
(e) Determine the electric field strength at the position(s) you have indicated in part (d) in terms of Q,L, and fundamental constants, as appropriate.
(f) Given that one-eighth of the sphere at point A is inside the surface, calculate the electric flux through face CDEF.