156 Week 4: Capacitance
Problem 7.
You are given a square parallel plate capacitor of sideLand plate separationdand a slab of
dielectric material with relative dielectric permittivityǫrthat exactly fills the volume between the
plates if fully inserted. At the moment, however, the slab is insertedonly a distancex. The capacitor
has aconstantfree chargeQ 0 on it.
a) Find the potential energy of the partially filled capacitor, as a function ofQ 0 , L, d, ǫ 0 , ǫrand
x.b) Is the potential energy minimal when the dielectric slab is fully inserted or fully removed?
Explain why.c) By using
Fx=−dU
dx
=find the force on the partially inserted dielectric slab. Does the force pull the dielectric slab
in (to fill the plate volume) or does it push it out from between the plates?d) Draw a simple picture involving the probable bound charge distribution on the partially in-
serted dielectric slab that physically explains this force.