Next: Electrostatic Fields
Up: Maxwell's Equations
Previous: Electromagnetic Momentum Conservation
 Demonstrate that the energy contained in the magnetic field generated by a stationary current distribution
in vacuum
is given by
 A transverse plane wave is incident normally in vacuum on a perfectly absorbing flat screen. Show that the
pressure exerted on the screen is equal to the electromagnetic energy density of the wave.
 Consider an infinite parallelplate capacitor. Let the lower plate lie at
, and carry the charge density
.
Likewise, let the upper plate lie at
, and carry the charge density
. Calculate the electromagnetic
momentum flux across the

plane. Hence, determine the direction and magnitude of the force per unit area
that the plates exert on one another.
 The equation of electromagnetic angular momentum conservation takes the general form
where
is the electromagnetic angular momentum density, and the tensor
is the electromagnetic angular
momentum flux. Demonstrate
that
and
where
is the electromagnetic momentum density, and
the electromagnetic momentum flux tensor.
 A long solenoid of radius
, with
turn per unit length, carries a steady current
. Two hollow
cylinders of length
are fixed coaxially such that they are free to rotate. The first cylinder, whose radius is
,
carries the uniformly distributed electric charge
. The second cylinder, whose radius is
, carries the
uniformly distributed electric charge
. Both cylinders are initially stationary. When the current is switched off the cylinders
start to rotate. Find the final angular momenta of the two cylinders, and demonstrate that the total angular momentum
of the system is the same before and after the current is switched off.
 Consider a system consisting of an electric charge
and a magnetic monopole
separated by a
distance
. Demonstrate that the total angular momentum stored in the resulting electromagnetic fields is
[Hint: The radial magnetic field generated a distance
from a magnetic monopole of strength
is of magnitude
.]
Next: Electrostatic Fields
Up: Maxwell's Equations
Previous: Electromagnetic Momentum Conservation
Richard Fitzpatrick
20140627