Homework 14 Due April 24 2007
1) A
LL
×
square slab with thickness
d
of dielectric with dielectric constant
κ
is partially
inserted a distance
x
between the plates of a parallel plate capacitor as shown below. The
plates are also squares of dimension
×
and are separated by a distance
dL
±
.
(a) If the capacitor is connected to a battery with emf
0
V
, what is the charge stored in this
capacitor as a function of
x
?
(b) In the situation of part (a), what is the electric potential energy stored in this capacitor
as a function of
x
?
(c) In the situation of part (a), if the dielectric is moving in the xdirection at a velocity v,
what is the current flowing through the wire at point P?
(d) In the situation of part (a), how much work does the battery do when the slab is
moved from the position
x
=0 to
x
=
L
? Show that this is twice the change in the stored
energy of the capacitor as the slab moves from
x
=0 to
x
=
L
.
(e) Explain how the result in part (d) is consistent with the law of conservation of energy.
In particular explain why this implies that a force is exerted on the slab. Which direction
is the force?
(f) Now consider the slightly different situation where the same capacitor is disconnect
but has a charge
0
Q
stored on the plates. What is the potential difference between the
plates as a function of
x
?
(g) In the situation of part (f), what is the electric potential energy stored in the capacitor
as a function of the position
x
?
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 Spring '08
 HerreraSiklody
 Electric Potential, Energy, Potential Energy, Work, Parallel Plate Capacitor, Ceff

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