A ring of radius is bent from copper wire of radius and cooled to

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits

The Boundary-Value Problem, Ch Magnetic diffusion, shielding and flux exclusion

Problem

A ring of radius

b = 2.0\,\mathrm{cm}

is bent from copper wire of radius

r_w = 0.50\,\mathrm{mm}

and cooled to

4\,\mathrm{K}

, where its conductivity is

\sigma = 5.96\times10^9\,\mathrm{S\,m^{-1}}

. ((a)) Using the thin-ring estimate

\mathcal{L}\approx\mu_0b[\ln(8b/r_w)-2]

and

R = 2b/\sigma r_w^2

, find the time constant

\mathcal{L}/R

with which a current in the ring decays. ((b)) The ring is cooled in a steady uniform field of

10\,\mathrm{mT}

perpendicular to its plane, and the field is then switched off. Say whether any flux through the copper ring is left one second later. ((c)) Now take the ring to be a perfect conductor, cooled in the same field before the field is switched off. Find the flux through it afterwards, explain from Faraday's law why it cannot change, and say how this differs from flux expulsion.

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