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A cylindrically symmetric magnetic field directed along the axis of a cylinder varies with time as B = k*t. An electron is released from rest at a distance r from the axis. Immediately after release, what is the magnitude of its acceleration? (e and m are the electron's charge magnitude and mass.)

1. e*k*r/(2*m)
2. e*k*r/m
3. 2*e*k*r/m
4. e*k*r²/(2*m)

Correct answer: e*k*r/(2*m)

Solution

The changing magnetic field induces a circular electric field. By Faraday's law over a circle of radius r: E*(2*pi*r) = pi*r²*(dB/dt), giving E = (r/2)*(dB/dt) = (r/2)*k. The force on the electron is F = eE, so acceleration a = eE/m = e*k*r/(2*m). (At the instant of release the electron is at rest, so the magnetic force is zero and only the induced electric force acts.)

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