An infinitely long straight wire carrying current $I$, a 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:
Answer: (D) $\dfrac{\mu_0}{2\pi}\dfrac{Ivl}{Rr}$
At the position of the connector the field of the wire is $B = \dfrac{\mu_0 I}{2\pi r}$, perpendicular to the plane.
The moving connector has motional emf $\varepsilon = Bvl = \dfrac{\mu_0 Ivl}{2\pi r}$.
The only resistance in the loop is $R$, so
$$i = \frac{\varepsilon}{R} = \frac{\mu_0}{2\pi}\frac{Ivl}{Rr}$$
Solution by Sreeraj P, M.Sc Physics