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STD 12 -6. Electromagnetic induction — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 -6. Electromagnetic induction4 Marks
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
✓

Answer

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

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

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

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

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

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