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 same sense.

Step-by-step solution

The magnetic field at the centre of a circular coil 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 same sense, the magnetic fields are in the same direction. The net magnetic field is: B = B₁ + B₂ = 4 10⁻⁴ + 4 10⁻⁴ = 8 10⁻⁴ T