Phys 3327 Fall 2010
HW 5
Due Wednesday 10/6/10 in lecture
Homework 5
Dynamic Electromagnetism
Ex. 5.1: Capacitor
Consider a parallelplate capacitor consisting of two large parallel perfectly conducting discs
a distance
d
apart and separated by a vacuum. The discs have radius
a
. At time
t
= 0, the
capacitor is connected to a battery, such that a constant current
i
starts to flow onto the
upper plate. (The same current flows out of the lower plate.) When answering the questions
below you may neglect edge effects. You may give all your answers to leading order in the
small ratio
a/ct
.
a) What are the electric and magnetic fields in the space between the capacitor plates,
as a function of time? Be sure to specify magnitude and direction.
b) Calculate the total field energy density for the space between the capacitor plates. Do
the electric and magnetic fields contribute equally to the energy density?
Hint: use the inequality
t
a/c
.
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 '10
 Cohen
 Magnetism, Energy, Work, Magnetic Field, loop, Maxwell stress tensor, Marion ex

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