St. Vincent College
PH 252: Electromagnetic Fields
Exam IV
11/6/2006
1. (30 pts) A sphere of radius Rcarries charge density ρ(r) = kr. Compute the energy in this charge
configuration in whatever way you wish.
2. (30 pts)
a) Starting with the basic definition of work and the force on a charged particle due to an electric field,
show that the energy required to assemble an arrangement of Ncharges point particles is
W=1
4πǫ0
N−1
X
i=1
N
X
j=i+1
qiqj
rij
b) Explain the argument that allows this sum to be rewritten as
W=1
8πǫ0
N
X
i=1
X
j6=i
qiqj
rij
3. (30 pts) A parallel plate capacitor is made with a composite dielectric. A sheet of dielectric of
permittivity ǫ1and thickness d1is placed on top of a second dielectric sheet of permittivity ǫ2and
thickness d2. This combination of dielectrics is placed between parallel conducting plates separated by
the distance d1+d2. What is the capacitance per unit plate area of this capacitor?
4. (10 pts) Explain why the expression for force is different for the two cases of (a) an isolated system
with constant charge and (b) a system kept at a constant potential.