Question

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

• A. Approximate magnitude of induced EMF generated in smaller loop when x = NR is $\frac{5}{2}\frac{{\mu }_{0}i\pi r^2}{N^4{R}^2}$ (where N is a positive constant)
• B. Approximate magnitude of induced EMF generated in smaller loop when x = NR is $\frac{3}{2}\frac{{\mu }_{0}i\pi r^{2}v}{N^4{R}^2}$ (where N is a positive constant)
• C. Direction of induced current in the smaller loop is same as that larger loop
• D. Direction of induced current in the smaller loop is opposite to that in larger loop.

Answer 1

Answer: (B), (C)

The correct options are
B

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

C

Direction of induced current in the smaller loop is same as that larger loop

$B=\frac{{\mu }_{0}i{R}^2}{2x^3}(x>>R);{\varphi }_0\frac{{\mu }_{0}i{R}^2\pi r^2}{2x^3}\Rightarrow \epsilon =\frac{-d{\varphi }_B}{dt}=\frac{3{\mu }_{0}i{R}^2\pi r^2}{2x^4}\frac{dx}{dt}=\frac{3}{2}\frac{{\mu }_{0}i\pi r^{2}v}{n^4{R}^2}$