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An infinitely long straight wire carries current I. In the same plane lie a single-sided open rectangular loop and a conductor C fitted with a sliding connector of length l and resistance R. The connector slides to the right with velocity v. The resistance of the rails and the self-inductance of the loop are negligible. The induced current in the loop, as a function of the separation r between the connector and the long wire, is:

1. (mu0/2pi) * I*v*l/(R*r)
2. (mu0/pi) * I*v*l/(R*r)
3. (2*mu0/pi) * I*v*l/(R*r)
4. (mu0/4pi) * I*v*l/(R*r)

Correct answer: (mu0/2pi) * I*v*l/(R*r)

Solution

The magnetic field of the long straight wire at the connector's distance r is B = mu0*I/(2*pi*r). The connector of length l moving with velocity v develops a motional EMF = B*l*v = mu0*I*l*v/(2*pi*r). The induced current is this EMF divided by R: i = mu0*I*v*l/(2*pi*R*r) = (mu0/2pi) * I*v*l/(R*r).

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