Two concentric circular coils $\mathrm{A}$ and $\mathrm{B}$ have radii $20 \mathrm{~cm}$ and $10…
Two concentric circular coils $\mathrm{A}$ and $\mathrm{B}$ have radii $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively lie in the same plane. The current in coil A is $0.5 \mathrm{~A}$ in anticlockwise direction. The current in coil B so that net field at the common centre is zero, is
$0.5 \mathrm{~A}$ in anticlockwise direction
$0.25 \mathrm{~A}$ in anticlockwise direction.
$0.25 \mathrm{~A}$ in clockwise direction.
$0.125 \mathrm{~A}$ in clockwise direction.
Solution
Magnetic field at the centre of a circular loop
$\mathrm{B}=\frac{\mu_0 \mathrm{NI}}{2 \mathrm{R}}$
Net Magneitc field $B_{\text {net }}=0$
(given)
$\begin{aligned} & \Rightarrow B_{\text {net }}=\frac{\mu_0 \mathrm{~N}_1 \times 0.5}{2 \times(0.2)}-\frac{\mu_0 \mathrm{~N}_1 \times \mathrm{x}}{2 \times(0 \cdot 1)} \\ & \Rightarrow \frac{\mu_0 \mathrm{~N}_1 \mathrm{x}}{0.2}=\frac{\mu_0 \mathrm{~N}_1 0.5}{0.4} \\ \therefore \quad & x=\frac{0.5 \times 0.2}{0.4} \\ & =0.25 \mathrm{~A} \text { in clockwise direction }\end{aligned}$