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A small square loop of edge Length a and resistance R is moved with velocity v₀away from an infinitely long current carrying conductor carrying current i so that the conductor and side of square are always in same plane. Find induced culrent in loop at a separation of r.

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$\frac{μ_{0} i a^{2} v}{π r^{2} R}$

$\frac{μ_{0} i a^{2} v}{4 π r^{2} R}$

$\frac{μ_{0} i a^{2} v}{2 π r^{2} R}$

$\frac{μ_{0} i a^{2} v}{2 π r R}$

answer is C.

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Detailed Solution

$ϕ = B A = \frac{μ_{0} i}{2 π v t} a^{2}$

$i = - \frac{1}{R} \frac{d ϕ}{d t} = \frac{μ_{0} i a^{2}}{2 π v t^{2} R} = \frac{μ_{0} i a^{2} v}{2 π r^{2} R}$

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