A large circular coil of 100 turns and radius 10 cm carrying a current of 2 A is placed in the y-z plane. The current in this coil is in the anticlockwise sense as seen from the positive x-axis. A small circular loop of radius 1 cm carrying a current of 5 A is placed on the x-axis at a distance of 10 3 cm from the centre of the large coil. The small loop is in the x-z plane and its current is in the clockwise sense a

Step-by-step solution

First, we find the magnetic field produced by the large coil at the position of the small loop. The magnetic field on the axis of a circular coil is B = ₀ N I₁ R^2 2(R^2 + x^2)^ 3/2 . Given N = 100 , I₁ = 2 A, R = 0.1 m, and x = 0.1 3 m. R^2 + x^2 = 0.01 + 0.03 = 0.04 m ^2 . B = 4 10⁻⁷ 100 2 0.01 2(0.04)^ 3/2 = 8 10⁻⁷ 2 0.008 = 5 10⁻⁵ T. Since the current is anticlockwise as seen from the positive x-axis, the magnetic field is directed along the positive x-axis: B = 5 10⁻⁵ i T. Next, we find the magnetic moment of