Suppose that you had an electric charge qe and a magnetic monopoleqm. The eld of the electric
charge is given by
E =
1
40
qe
r2 ^r: (5)
Suppose the eld of the magnetic monopole is
B =
0
4
qm
r2 ^r: (6)
Assume the two charges are separated by a distance d { you canplace the electric charge at the origin
and the magnetic charge a distance d away from the origin on thez-axis. Show that the total angular
momentum stored in the elds is (remarkably, independent of d and)equal to
Lem =
0
4
qeqm: (7)
Doing so requires a little work, but the result is worth it. Startby using the law of cosines to express
the B eld in terms of the radial coordinate r and the ^r and ^zunit vectors. Why is the result so cool?
Quantum mechanics requires quantization of L in units of h. Thiswould imply that that product
qeqm must be quantized. If there existed a magnetic monopole withmagnetic charge qm, quantum
mechanics could be used to explain the quantization of electriccharge we observe in nature.
Suppose that you had an electric charge qe and a magnetic monopoleqm. The eld of the electric
charge is given by
E =
1
40
qe
r2 ^r: (5)
Suppose the eld of the magnetic monopole is
B =
0
4
qm
r2 ^r: (6)
Assume the two charges are separated by a distance d { you canplace the electric charge at the origin
and the magnetic charge a distance d away from the origin on thez-axis. Show that the total angular
momentum stored in the elds is (remarkably, independent of d and)equal to
Lem =
0
4
qeqm: (7)
Doing so requires a little work, but the result is worth it. Startby using the law of cosines to express
the B eld in terms of the radial coordinate r and the ^r and ^zunit vectors. Why is the result so cool?
Quantum mechanics requires quantization of L in units of h. Thiswould imply that that product
qeqm must be quantized. If there existed a magnetic monopole withmagnetic charge qm, quantum
mechanics could be used to explain the quantization of electriccharge we observe in nature.
