Electromotive force and current induced by a bar magnet and a monopole

The magnetic flux $\Phi_{\mathrm{B}}$, electromotive force, EMF, and current $I_{\mathrm{in}}$, induced by a moving magnetic bar and an imaginary magnetic monopole in a superconducting loop of one turn, are numerically calculated. The magnetic field of the bar magnet is approximated with the magnetic field along $z$ axis of a solenoid with length $l$ and radius $a$ with current $I$, while the magnetic field of the monopole is supposed to be inversely proportional to $r^{\mathrm{2}}$. Calculations show that, for a bar magnet, $\Phi_{\mathrm{B}}$ and $I_{\mathrm{in}}$ reach the maximum when the bar is at the center of the superconducting loop, but sign of EMF changes. The calculation doesn't contradict our experiment results which show that $I_{\mathrm{in}}$ switches sign as EMF does since in the laboratory the loop is not superconducting. For a magnetic monopole, $\Phi _{\mathrm{B}}$ is discontinuous (from positive maximum to negative maximum) when the bar moves through the center of the superconducting loop, so the there is a delta function in EMF in addition to EMF induced by the a moving monopole. The current $I_{\mathrm{in}}$ is continuous at this moment and continues to grow while the monopole leaves the loop. The calculations about the monopole agree with published results.