Two concentric circular coils \(A\) and \(B\) having radii 20 cm and 10 cm respectively lie in the same plane. The current in coil A is 0.5 A in anticlockwise direction. The current in coil B, so that net magnetic field at the common centre is zero, is

Given data: \(\mathrm{R}_1=0.20 \mathrm{~m}, \mathrm{I}_1=0.5 \mathrm{~A}, \mathrm{R}_2=0.10 \mathrm{~m}\) The formula for magnetic field at the centre of the coil is \(B=\frac{\mu_0 I}{2 R}\)
For coil \(A: B_A=\frac{\mu_0 I_1}{2 R_1}\)
For coil B: \(B_B=\frac{\mu_0 I_2}{2 R_2}\)
For net magnetic field to be zero, the magnitude of the field should be equal and the direction of the current should be opposite. Hence, the current in the coil B should be in clockwise direction.
\(\begin{aligned}
& \frac{\mu_0 I_1}{2 R_1}=\frac{\mu_0 I_2}{2 R_2} \\
\therefore \quad & I_2=\frac{I_1 R_2}{R_1}=\frac{0.5 \times 0.10}{0.20}=0.25 \mathrm{~A}
\end{aligned}\)