Problem 5. A neutral spherical conductor of radius R is placed in a uniform external field E .
0
(a) Since electrostatic fields must vanish inside conductors, the surface charge on the conductor
must conspire to create an opposing uniform field inside it. How exactly does this happen?
Specifically, explicitly find σ(θ), the surface charge density as a function of the angle from E .
0
(Hint: we’re already seen an example of a suitable charge density in E1.)
(b) Now let’s consider the field created by this surface charge outside the sphere. We could
integrate the answer to part (a), but it’s even easier to use the method of images. Suppose
that the original external field E was created by two very distant opposite point charges.
0
Argue that the sphere picks up a dipole moment, and find its magnitude.
(c) What happens to the argument of part (b) if we instead suppose that E was created by a
0
single very distant point charge?
This lessons of this problem will be useful in several later handouts.