98 Week 2: Continuous Charge and Gauss’s Law
Problem 7.
a
b
+q
A spherical conducting shell with zero net charge has inner radiusaand outer radiusb. A point
chargeqis placed at the center of the shell.
a) Use Gauss’s Law and the properties of conductors in equilibrium tofind the electric field in
the regionsr < a,a < r < b,b < r.b) Find the charge density on the inner and outer surfaces of the shell.Problem 8.
A conducting neutral sphere of radiusRis placed in a uniform electric fieldE~=E 0 zˆ. Using
Gauss’s Law and the properties of conductors in equilibrium,draw a qualitatively correct represen-
tationof the electric field that results. Also indicate on the figure the qualitative distribution of
charge on the surface of the conductor one might expect as its charge polarizes in response to the
external field. Is there more charge near the “equator” or the poles?