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If magnetic monopoles exist, they are predicted to have large charges--or equivalently, a large coupling constant, which means that perturbative models don't converge.

While I get that that makes it very difficult to calculate things like the binding energy of monopolium, is it at least possible to make qualitative statements about what magnetostatics, the strongly-coupled analog of electrostatics, looks like? E.g., can you still reasonably approximate the strength of a monopole field as $\frac{1}{r^2}$ down to arbitrarily small lengths?

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  • $\begingroup$ Yes; what of it? $\endgroup$ Sep 18, 2021 at 19:55

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The magnetic monopole acts exactly like an electric monopole. In magnetostatics, the equation of interest

($\mu_0=1$):

$$\nabla \cdot \vec{B} = \rho$$

where $\rho$ is the magnetic charge density, has a solution:

$$\vec{B} = \frac{1}{4\pi}\frac{q}{r^2}$$

for point particles, i.e: $\rho = \delta(r)$, and $q$ is the magnetic charge. In fact, this is exactly what we want. We designed the magnetic monopole to act like a electric monopole because we saw it would be nice to have symmetry between them.

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