Answers for E4 (rev. 3.0)
Questions for discussion
1. In Physics 7B problems, we commonly consider “a ball of charge, with uniform charge per unit
volume ρ.” How do you know that the ball in such a problem is made of non-conducting material,
such as plastic?
If the ball were made of conducting material, then all of that excess charge would quickly migrate
to the surface of the ball. When everything settled down, we would no longer have a volume
charge distribution, but rather a surface charge distribution.
2. Give an intuitive justification for each of the following facts about conductors, all of which hold in
a) Within a conducting material, the electric field vanishes.
Intuitively speaking, if the electric field at some point in the material were not zero, then the
mobile charges within the material would undergo some acceleration, and they would slosh
around inside the material. But we are assuming that everything has settled into equilibrium, so
the particles can no longer be accelerating. Hence the field within the material must be zero.
b) Any net charge on a conductor must reside on a surface of the conductor.
Intuitively speaking, if there were some bit of charge q located within the material proper, then we
could draw a small Gaussian surface around that bit. (The surface should be small enough so that
every point of the surface lies within the conducting material itself.) Gauss's Law would then
imply that the net flux outward through our surface is q/ε0. However, computing the flux directly,
we see that since the electric field is zero at all points of the surface, we get ΦE = 0. This
contradiction shows that there cannot be any charge within the conducting material itself.
c) The electric field at a surface of a conductor is always perpendicular to the conducting surface.
Imagine what would happen if the field at a surface were not perpendicular to the surface. Then
there would be some tange