Two concentric circular coils A and B having | vedclass

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(C) Given data: $R_A = 0.20 \ m$,$I_A = 0.5 \ A$,$R_B = 0.10 \ m$. The formula for the magnetic field at the centre of a circular coil is $B = \frac{\

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$0.25 \ A$ in clockwise direction.

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(C) Given data: $R_A = 0.20 \ m$,$I_A = 0.5 \ A$,$R_B = 0.10 \ m$. The formula for the magnetic field at the centre of a circular coil is $B = \frac{\mu_0 I}{2 R}$. For coil $A$: $B_A = \frac{\mu_0 I_A}{2 R_A}$. For coil $B$: $B_B = \frac{\mu_0 I_B}{2 R_B}$. For the net magnetic field at the common centre to be zero,the magnitudes of the magnetic fields produced by both coils must be equal,and their directions must be opposite. Since the current in coil $A$ is in the anticlockwise direction,the current in coil $B$ must be in the clockwise direction. Equating the magnitudes: $\frac{\mu_0 I_A}{2 R_A} = \frac{\mu_0 I_B}{2 R_B}$. Therefore,$I_B = I_A 	imes \frac{R_B}{R_A} = 0.5 	imes \frac{0.10}{0.20} = 0.25 \ A$. Thus,the current in coil $B$ is $0.25 \ A$ in the clockwise direction.

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

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