A copper pipe of mean radius and wall thickness (conductivity ) carries the eddy…

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 copper pipe of mean radius

a = 10\,\mathrm{mm}

and wall thickness

d = 1.5\,\mathrm{mm}

(conductivity

\sigma = 5.96\times10^7\,\mathrm{S\,m^{-1}}

) carries the eddy currents induced by a magnet falling at

v = 0.20\,\mathrm{m\,s^{-1}}

. ((a)) Calculate the wall's own diffusion time,

\mu_0\sigma ad

. ((b)) Calculate the time

a/v

over which the flux through one ring of the wall rises and falls as the magnet passes, and show that the ratio of the two times is the magnetic Reynolds number of the wall,

R_m = \mu_0\sigma vd

. ((c)) State what this small ratio justifies about the eddy-current model.

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