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EE 151
Caltech
Electromagnetic Engineering
Spring ‘05
Homework 3
Due Tuesday, April 19
th
in class
1.
An ideal parallel-plate capacitor is shown in
Fig. 1
. The radius of each plate is a. The
spacing between the two plates is h. A time-varying voltage V(t) = V
0
sin(
ω
t) is applied across
the capacitor.
Assume uniform field inside the capacitor and ignore fringing effects.
(a)
A rectangular-shaped open metal loop is inserted in the capacitor. The surface of
the loop is parallel to the axis of the capacitor. The dimensions of the loop are
width
w
and length
l
. The insertion depth is
b
. Calculate the induced voltage V
ind
across the loop.
(b)
Show that
Where
U
(t) is the total electromagnetic energy stored inside the capacitor,
E
and
H
are, respectively, the electric and magnetic field vector. The integral is evaluated over
the surface that encloses the volume between the two circular plates.
b
w
a
l
V
inc
Figure 1

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