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Question 7.5: A long cylindrical magnet of length L and radius a carries a...

A long cylindrical magnet of length L and radius a carries a uniform magnetization M parallel to its axis. It passes at constant velocity v through a circular wire ring of slightly larger diameter (Fig. 7.22). Graph the emf induced in the ring, as a function of time.

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The magnetic field is the same as that of a long solenoid with surface current \pmb{K}b = M \hat{\phi} . So the field inside is \pmb{B} = μ_0\pmb{M}, except near the ends, where it starts to spread out. The flux through the ring is zero when the magnet is far away; it builds up to a maximum of   μ_{0}M\pi a^{2}  as the leading end passes through; and it drops back to zero as the trailing end emerges (Fig. 7.23a). The emf is (minus) the derivative of Φ with respect to time, so it consists of two spikes, as shown in Fig. 7.23b.

7.23

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