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

Step-by-step solution

Given data: R ₁=0.20 ~m , I ₁=0.5 ~A , R ₂=0.10 ~m The formula for magnetic field at the centre of the coil is B= ₀ I 2 R For coil A: B_A= ₀ I₁ 2 R₁ For coil B: B_B= ₀ I₂ 2 R₂ 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. aligned & ₀ I₁ 2 R₁ = ₀ I₂ 2 R₂ & I₂= I₁ R₂ R₁ = 0.5 0.10 0.20 =0.25 ~A aligned