A superconducting wire loop of radius a is centred at the origin in a plane. A magnetic dipole of moment m is brought from infinity along the loop's axis toward the centre, its north pole pointing at the loop, stopping at a distance r (with r a). The on-axis field of a dipole at distanc

Question

A superconducting wire loop of radius a is centred at the origin in a plane. A magnetic dipole of moment m is brought from infinity along the loop's axis toward the centre, its north pole pointing at the loop, stopping at a distance r (with r >> a). The on-axis field of a dipole at distance r is (mu0/(2*pi))*(m/r³). Using this, what is the proportionality of the magnetic flux that the external dipole would produce through the loop (taken as a flat disc of radius a) just before the superconductor's own induced current responds?

Accepted Answer

m/r³. The flux through the small loop from the external dipole is the (nearly uniform) axial field of the dipole multiplied by the loop area pi*a². Since the axial field of a dipole goes as m/r³, the flux is proportional to m/r³. The superconductor then induces a current to cancel any change in this flux, but the question asks only for the scaling of the imposed flux.

Solution

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