I am trying to calculate the current induced in a loop assuming a magnetic monopole exists. The loop is a perfect conductor, which I understand implies the electric field inside must be zero. I picture the problem with the magnetic monopole traveling with a velocity coaxial with the loop. I am given the loop has a self inductance L, so what I've done is take Faraday's law (modified for the existance of a mag. monopole), and the current density I'm associating as follows(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \vec{\nabla} \wedge \vec{E} =0= -\left\{ \mu_{0} \vec{j}_{m}+\frac{\partial \vec{B}}{\partial t} \right\}[/tex]

Yielding

[tex] \mu_{0} \vec{j}_{m} = -\frac{\partial \vec{B} }{\partial t} [/tex]

Now relating to the induced emf I have

[tex] -L\frac{dI}{dt} = -\dot{\phi}_{m} = \int -\frac{\partial \vec{B}}{\partial t} \cdot d\vec{a} [/tex]

From which I make the identification

[tex] \vec{j}_{m} = \rho_{m} \vec{v} [/tex]

Which gives assuming a planar area loop with the direction of the velocity being parallel to the loop is given by

[tex] -L \frac{dI}{dt} = \mu_{0} \rho_{m} A_{loop} v

\Rightarrow -L\frac{dI}{dt} =\mu_{0} \rho_{m} A_{loop} \frac{dz}{dt} [/tex]

which is where I am stuck. I think I want to integrate over a long time, including the point and past the point the magnetic monopole passes through the loop. My question(s) is does everything I have done so far make sense, and if so where do I go from here?

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# Homework Help: Magnetic monopole induces current in perfect conducting ring

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