An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown in the figure. The connector ha

Question

An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor $C$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length l. and resistance $R$ . It slides to the right with a velocity $v$ . The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is

TestHub · Accepted Answer

The induced current in the wire will be due to the motional EMF developed in the moving resistor and that back emf developed at that point will be equal to $V B L$

$V =$ velocity of the conductor

$B =$ perpendicular magnetic field

$L =$ length of conductor

We know magnetic field due to a long wire is

$B = \frac{μ_{0} i}{2 π r}$

Hence the induced current across wire will be :

$I = \frac{e}{R}$

$I = \frac{μ_{0}}{2 π} \frac{Iv ℓ}{Rr}$

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