Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A . The coils have 50 and 100 turns respectively and are positioned so that their planes and centres coincide. Determine the magnitude of the magnetic field B at the common centre of the coils if the currents flow in the opposite sense.

Step-by-step solution

The magnetic field at the centre of a circular coil of N turns, radius r , and carrying current I is given by B = ₀ N I 2r . For the first coil: B₁ = ₀ N₁ I₁ 2r₁ = 4 10⁻⁷ 50 2.0 2 0.05 = 4 10⁻⁴ T For the second coil: B₂ = ₀ N₂ I₂ 2r₂ = 4 10⁻⁷ 100 2.0 2 0.10 = 4 10⁻⁴ T Since the currents flow in the opposite sense, the magnetic fields produced by the two coils at their common centre are in opposite directions. The net magnetic field is B = |B₁ - B₂| = 4 10⁻⁴ - 4 10⁻⁴ = 0 .