A rectangular loop of length l and breadth b | vedclass

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(C) The magnetic field $B$ at a distance $r$ from an infinitely long wire is given by $B = \frac{\mu_0 i}{2 \pi r}$.The loop has two sides of length $

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$\frac{\mu_0 i l b v}{2 \pi x(l+x)}$

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(C) The magnetic field $B$ at a distance $r$ from an infinitely long wire is given by $B = \frac{\mu_0 i}{2 \pi r}$.The loop has two sides of length $b$ parallel to the wire at distances $x$ and $x+l$ from the wire.The motional emf induced in a conductor moving in a magnetic field is $e = B v L$.The emf induced in the side at distance $x$ is $e_1 = B_1 v b = \left(\frac{\mu_0 i}{2 \pi x}\right) v b$.The emf induced in the side at distance $x+l$ is $e_2 = B_2 v b = \left(\frac{\mu_0 i}{2 \pi (x+l)}\right) v b$.Since the loop moves away,these emfs oppose each other. The net magnitude of the emf is $|e| = |e_1 - e_2|$.$|e| = \frac{\mu_0 i v b}{2 \pi} \left( \frac{1}{x} - \frac{1}{x+l} \right) = \frac{\mu_0 i v b}{2 \pi} \left( \frac{x+l-x}{x(x+l)} \right) = \frac{\mu_0 i l b v}{2 \pi x(x+l)}$.

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