Magnetic Monopoles & Gauss' Law for Magnetism
Physics is not about how the world is, it is about what we
can say about the world"
- In our initial discussion of magnetism we made the point that
we were going to treat magnetism in a similar way to
electricity. However, whereas our discussion of
electricity began with electric charges and the electric field
associated with these charges, the magnetic discussion started
with the existence of the magnetic field. No mention was
made of "magnetic charges", which would play the same role in
magnetism as electric charges in electricity. This is
because individual magnetic charges - magnetic monopoles
- are apparently impossible to isolate.
- The simplest magnetic object we have been able to isolate is
the magnetic dipole.
Current loops, bar magnets and solenoids all produce
dipole fields with a characteristic magnetic dipole moment.
- The bar magnetic may be considered to be a combination of two
magnetic monopoles, usually labelled North and South. This
is similar to the electric dipole comprised of equal but
opposite electric charges.
- Whereas with the
electric dipole it is possible to isolate the positive and
negative charges, experimentally it is not possible to
separate the North and South poles of a bar magnet.
Break a magnet in two and you get two magnets, each with a
North and South pole. Continuing this splitting
process down to the atomic level we find that even
elementary particles behave as magnetic dipoles, each with a
North and South pole. It appears that nature does not
allow us to create magnetic monopoles in this way.
- However, theoreticians
developing unified quantum theories of the Universe,
so-called "Theories of Everything", are almost unanimous in
the necessity for magnetic monopoles as elementary particles
created shortly after the birth of the Universe.
The belief is that shortly after their creation, magnetic
monopoles were "frozen out" - meaning that their
interactions with the rest of the matter in the Universe is
highly suppressed. This does not prevent physicists
from searching for evidence for the existence of magnetic
Gauss' Law for Magnetism
- So far we have discussed three basic equations
describing electromagnetic phenomena - the first three
of Maxwell's equations.
- Gauss' Law involves the flux integral for the
electric field. To complete the correspondence
between electricity and magnetism we expect a fourth
equation involving the magnetic flux - "Gauss' Law
- The right hand side of Gauss' Law includes a
summation over electric charges. Therefore,
for magnetism, we expect a summation over "magnetic
charges". But magnetic charges, North and
South poles (equivalent to positive and negative
electric charges) always exist in pairs, the net
"magnetic charge" is thus always zero. Gauss'
Law for Magnetism must therefore take the form,
the flux of B
closed surface is zero.
Note that the fact that
the surface is closed is very important ! A
magnetic flux integral appears in Faraday's
Law - in this case the surface is generally not
Electric field lines begin
(positive) and end (negative) on charges.
Since there are no magnetic charges magnetic field
lines form closed loops.
A Princeton plasma physicist is at the beach when he
discovers an ancient looking oil lantern sticking out of the
sand. He rubs the sand off with a towel and a genie pops
out. The genie offers to grant him one wish. The physicist
retrieves a map of the world from his car an circles the
Middle East and tells the genie, 'I wish you to bring peace
in this region'.
After 10 long minutes of deliberation, the genie replies,
'Gee, there are lots of problems there with Lebanon, Iraq,
Israel, and all those other places. This is awfully
embarrassing. I've never had to do this before, but I'm just
going to have to ask you for another wish. This one is just
too much for me'.
Taken aback, the physicist thinks a bit and asks, 'I wish
that the Princeton tokamak would achieve scientific fusion
After another deliberation the genie asks, 'Could I see that
Dr. C. L. Davis
University of Louisville