Two concentric coplanar circular coils, coil 1 and coil 2, have radii cm and 2 cm respectively. Coil 1 carries a current of 2 A and coil 2 carries a current of 3 A in the opposite direction. The magnitude of the net magnetic field at their common centre is (Take ₀ = 4 10⁻⁷ T m A ⁻¹ ):

Step-by-step solution

The magnetic field at the centre of a circular coil is given by B = ₀ I 2 R . For coil 1: B₁ = 4 10⁻⁷ 2 2 10⁻² = 4 10⁻⁵ T = 40 T For coil 2: B₂ = 4 10⁻⁷ 3 2 2 10⁻² = 3 10⁻⁵ T = 30 T Since the currents are in opposite directions, the magnetic fields at the centre will oppose each other. Net magnetic field: B_ net = |B₁ - B₂| = 40 T - 30 T = 10 T Answer: 10 T