Detecting Magnetic Monopoles with Induced Currents in a Wire Loop

[Charlie G]

Hi, I just submitted some homework that had a question that I'd really like to know the answer to now (rather than waiting on getting the homework back). The question asked to plot the current induced in a loop of wire as a magnetic monopole passed through it. My graph showed the current increasing exponentially as the monopole approached (I believed this to be the case since the rate that the flux changes is increasing as the distance is closed).

Once on the other side of the loop I thought the direction of the changes in the magnetic field would still point in the same direction as the approach so that the current still runs in the same direction but is decreasing exponentially now (whereas a dipole induces a current opposite in direction after passing through the center?)

So I suppose my question is this: when trying to detect magnetic monopoles by means of induced currents in a loop of wire, is the 'signal' for a monopole a first exponentially increasing current that then decreases exponentially, while the signal for the typical dipole is first an increasing current (growing quicker than with the monopole, since the field is 1/r^3) that changes direction and then decreases?


Also, just out of curiosity, another problem involved a superconducting ring moving along its' axis at a constant speed towards some point near the ring's axis (a distance y from the axis) and asked to determine the electric field induced at the point. Since E=emf/L and the emf has a factor y^2 (I used a ring of radius y around the axis as my 'flux surface', with area pi*y^2) and the length has y (2*pi*y = L) in it, my electric field was thus proportional to y, the distance from the axis of the superconducting ring.

This result seems incorrect to me, intuitively speaking it would seem the electric field would weaken as you move away from the ring's axis, but perhaps by expanding out you now have more magnetic field lines contributing to the flux, though this seemed spurious since I began only considering the magnetic field along the ring's axis, not anywhere else. So maybe one of you guys can tell me if the result I got was valid.

Thank you.

 

[Valerie Park]

In regards to your first question, yes, the signal for a magnetic monopole would be an exponentially increasing current that then decreases exponentially as it passes through the loop. The current will always flow in the same direction, and the magnitude of the current will decrease as the monopole passes through the loop. As for your second question, the electric field induced at the point, y, away from the superconducting ring's axis should indeed weaken as you move away from the ring's axis. This is because the magnetic flux through the surface area is decreasing with distance, so the induced EMF, and thus the electric field, is decreasing.