Two concentric coils, each of radius equal to 2 cm are placed at right angle to each other. If 3 A and 4 A are the currents flowing through the two coils, respectively. The magnetic induction (in Wb/m ^2 ) at the centre of the coils will be ₀ = 4 10⁻⁷ SI unit

Step-by-step solution

The magnetic field at the centre of a circular coil is given by B = ₀ I 2R . For the first coil, B₁ = ₀ I₁ 2R . For the second coil, B₂ = ₀ I₂ 2R . Since the coils are placed at right angles to each other, their magnetic fields at the centre are perpendicular. The resultant magnetic field is: B = B₁^2 + B₂^2 = ₀ 2R I₁^2 + I₂^2 Substituting the given values R = 2 10⁻² m, I₁ = 3 A, I₂ = 4 A, and ₀ = 4 10⁻⁷ T m/A: B = 4 10⁻⁷ 2 2 10⁻² 3^2 + 4^2 B = 4 10⁻⁷ 4 10⁻² 5 B = 10⁻⁵ 5 = 5 10⁻⁵ Wb/m ^2 Answer: 5 10⁻⁵