An infinitely long, straight wire carrying current I, one side opened… | JEE Main 2020 (5 Sep, Shift 2)

Q45JEE Main 2020 · 5 SEP · SHIFT 2Difficult

Motional EMF

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:

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Answer: (c)

Field of the long wire at the connector: $B = \dfrac{\mu_0 I}{2\pi r}$
Motional emf in the connector: $e = Blv = \dfrac{\mu_0 I l v}{2\pi r}$
Only resistance is $R$ , so $i = \dfrac{e}{R} = \dfrac{\mu_0}{2\pi}\dfrac{Ivl}{Rr}$
So the answer is (c).

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Motional EMF question from JEE Main 2020 (5 Sep, Shift 2)

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