Exercises with Magnetic Monopoles - Kurt Nalty

orbit. Some novelties are found, however. The orbital radius is not always
an equatorial radius. The electron can orbit at any arbitrary latitude.
The next observation is more interesting. A positive charge orbits a
positive monopole in a clockwise direction seen from further out, in the lower
density B region. If I magically reverse the direction of the electric charge
at a point, the new orbit is in a plane at right angles to the previous orbit.
A 180 degree change in initial conditions leads to a 90 degree change in the
solution. We still orbit in a clockwise direction about the radial flux. I find
this fascinating.
Here are the formulae for the orbital radius and acceleration of our planar
solution.
ρ = 1 κ
= v2
a
a = µq eq m
4π
1 v
m
ρ = mv 4πr2
µq e q m
r 2
We have a little gem hidden in this formula. Suggestively re-arranging
our equation, we have
ρ = mv 4πr2
µq e q m
mvr = µq eq m ρ
4π r
This shows that for the case of equatorial orbits, where ρ = r and L =
mvr, the classical angular momentum is equal to the field momentum of the
electric charge/magnetic monopole pair.
Minimum Radius for Equatorial Orbits
We have yet another gem hidden in this formula. The maximum value for
ρ is ρ = r for an equatorial orbit. Our speed for this system is constant.
Rather than looking for ρ, let’s find r as a function of speed and mass.
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