A conducting circular loop is placed in a uniform magnetic field of 0 . 4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm s - 1 . The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be _______ μV .

Step-by-step solution

The data given is B = 0 . 4   T R = 2 × 10 - 2   m It is given that d R d t = 10 - 3   m   s - 1 Area of the loop is A = π R 2 So, d A d t = 2 π R d R d t The flux is, ϕ = 2 π R d R d t × B So, the magnitude of emf is ε = 2 × 22 7 × 2 × 10 - 2 × 10 - 3 × 0 . 4 = 5 . 028 × 10 - 5   V = 50 . 28   μV ≈ 50     μV