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(C) The magnetic field at the centre of a circular coil is given by $B = \frac{\mu_0 I}{2R}$.For the net magnetic field at the common centre to be zer

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$0.25 	ext{ A}$ in the clockwise direction

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(C) The magnetic field at the centre of a circular coil is given by $B = \frac{\mu_0 I}{2R}$.For the net magnetic field at the common centre to be zero,the magnetic fields produced by coils $A$ and $B$ must be equal in magnitude and opposite in direction.Since coil $A$ has a current in the anticlockwise direction,its magnetic field points out of the plane. Therefore,coil $B$ must produce a magnetic field pointing into the plane,which requires a clockwise current.Let $I_A = 0.5 	ext{ A}$,$R_A = 0.2 	ext{ m}$,$R_B = 0.1 	ext{ m}$,and $I_B$ be the current in coil $B$.Setting the magnitudes equal: $\frac{\mu_0 I_A}{2 R_A} = \frac{\mu_0 I_B}{2 R_B}$.Substituting the values: $\frac{0.5}{0.2} = \frac{I_B}{0.1}$.$I_B = \frac{0.5 	imes 0.1}{0.2} = 0.25 	ext{ A}$.Thus,the current in coil $B$ is $0.25 	ext{ A}$ in the clockwise direction.

Two concentric circular coils $A$ and $B$ have radii $20 \text{ cm}$ and $10 \text{ cm}$ respectively and lie in the same plane. The current in coil $A$ is $0.5 \text{ A}$ in the anticlockwise direction. What is the current in coil $B$ such that the net magnetic field at the common centre is zero?

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