has units of
magnetization per unit volume and 
has units of
polarization per unit volume and that this is consistent with the units
of Maxwell's equations given 
has units amps
per m square and 
has units of
coul per 
. University of California
College of Engineering
Department of Electrical Engineering
and Computer Sciences
| T.K. Gustafson | Spring 1997 |
| EECS 117b | 4 units |
Electromagnetic Fields and Waves
Problem Set One:
1) Units
a) Show that has units of
magnetization per unit volume and has units of
polarization per unit volume and that this is consistent with the units
of Maxwell's equations given has units amps
per m square and has units of
coul per .
b) So what are the units of 
?
c) What is the definition of 
?
2) Guage If we choose a guage 
( Coulomb guage)
what are the equations for A and 
.
3) Consistency
Repeat the arguments given in the class that to have six equations in six
unknowns requires the "constituitive relations".
4) Dependent and Independent variables
Which are more fundamental 
and 
or 
and 
. ( Hint : The Aharanov and Bohm experiment)
5) Coulomb or Lorentz guage
Atomic physicists argue that one should use the Coulomb guage when calculating
the consequences of electromagnetic interactions with atoms ( or molecules)
and therefore arrays of atoms (crystals). Why? Why not the more symmetrical
Lorentz guage?
6) Dependent and independent variables We typically consider E
and H as independent variables. For example 
= voltage and
= current. Can
D and B be independent variables?
* 7) Force equation
We have been taught that the definition of E is given by f=qE.
Argue using relativity that more generally f=q(E+v
B) . Is this an approximation?