Two concentric circular coils A and B have 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 field at the common centre is zero, is

Step-by-step solution

Magnetic field at the centre of a circular loop B = ₀ NI 2 R Net Magneitc field B_ net =0 (given) aligned & B_ net = ₀ ~N ₁ 0.5 2 (0.2) - ₀ ~N ₁ x 2 (0 1) & ₀ ~N ₁ x 0.2 = ₀ ~N ₁ 0.5 0.4 & x= 0.5 0.2 0.4 & =0.25 ~A in clockwise direction aligned