Magnetic Monopoles & Gauss' Law for Magnetism

" Physics is not about how the world is, it is about what we can say about the world"
Niels Bohr

questionmark     Magnetic Monopoles    questionmark

magmonopolefig2    magmonopolefig3

mag_monopole_fig1                                           magintrofig3

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 monopoles.


Gauss' Law for Magnetism

  • So far we have discussed three basic equations describing electromagnetic phenomena - the first three of Maxwell's equations.
Gauss' Law:   elecgausseqn3

Ampere's Law:  magampereeqn1

Faraday's Law:  magfaradayeqn6
  • 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 for Magnetism".
  • 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 through a closed surface is zero.

exclamation 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 closed.

hot 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 energy break-even.'

After another deliberation the genie asks, 'Could I see that map again?' 


Dr. C. L. Davis
Physics Department
University of Louisville