Two coaxial circular loops are shown in figure, smaller loop (radius = r) is a distance x above the larger one (Radius = R) with x>>R. Now if x is changing at a constant rate $\frac{d x}{d t} = v > 0$ and current is flowing in the larger loop as shown then:

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Approximate magnitude of induced EMF generated in smaller loop when $x = N R i s \frac{3}{2} \frac{μ_{0} i π r^{2}}{N^{4} R^{2}}$ (where N is a positive constant)

Approximate magnitude of induced EMF generated in smaller loop when $x = N R i s \frac{3}{2} \frac{μ_{0} i π r^{2} v}{N^{4} R^{2}}$ (where N is a positive constant)

Direction of induced current in the smaller loop is same as that larger loop (as seen from below the larger loop)

Direction of induced current in the smaller loop is opposite to that in larger loop (as seen from below the larger loop)

answer is B, C.

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Detailed Solution

$B = \frac{μ_{0} i R^{2}}{2 x^{3}} (x > > R) ϕ_{0} = \frac{μ_{0} i R^{2} π r^{2}}{2 x^{3}} \Rightarrow ε = \frac{- d ϕ_{B}}{d t} = \frac{3 μ_{0} i R^{2} π r^{2}}{2 x^{4}} \frac{d x}{d t} = \frac{3}{2} \frac{μ_{0} π r^{2} v}{N^{4} R^{2}}$