Assuming that “Coulomb’s law” for magnetic charges \left(q_{m}\right) reads
F =\frac{\mu_{0}}{4 \pi} \frac{q_{m_{1}} q_{m_{2}}}{ᴫ^{2}} \hat{ ᴫ} (7.46)
work out the force law for a monopole qm moving with velocity v through electric and magnetic fields E and B ^{26}.
From \nabla \cdot B =\mu_{0} \rho_{m} it follows that the field of a point monopole is B =\frac{\mu_{0}}{4 \pi} \frac{q_{m}}{ᴫ^{2}} \hat{ ᴫ} . The force law has the form F \propto q_{m}\left( B -\frac{1}{c^{2}} v \times E \right) (see Prob. 5.22—the c^{2} is needed on dimensional grounds). The proportionality constant must be 1 to reproduce “Coulomb’s law” for point charges at rest. So F =q_{m}\left( B -\frac{1}{c^{2}} v \times E \right) .