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 & Solution

Correct Answer

(B) \(\frac{\mu_{0}}{2 \pi} \frac{ Ivl }{ Rr }\)

Detailed explanation

\(B =\frac{\mu_{0} i }{2 \pi r }\)

\(\phi=\frac{\mu_{0} i }{2 \pi r } \ell dr\)

\(\Rightarrow \frac{ d \phi}{ dt }=\frac{\mu_{0} i \ell}{2 \pi r } \cdot \frac{ dr }{ dt }\)

\(\Rightarrow e =\frac{\mu_{0}}{2 \pi} \cdot \frac{ iv \ell}{ r }\)

\(i =\frac{ e }{ R }=\frac{\mu_{0}}{2 \pi} \cdot \frac{ iv \ell}{ Rr }\)

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