A circular coil of radius 2.00 cm comprises 50 turns. A uniform magnetic field B = 0.200 T is present in the region, directed parallel to the axis of the loop. The coil is then rotated about a diameter by an angle of 60.0^ . The process takes 0.100 s . Determine the average emf induced in the coil.

Step-by-step solution

The initial magnetic flux through the coil is given by ₁ = N B A ₁ . Substituting the given values, N = 50 , B = 0.200 T , A = (0.02)^2 m ^2 , and ₁ = 0^ : ₁ = 50 0.200 (0.02)^2 1 = 0.004 Wb The final magnetic flux through the coil after rotation by 60^ is ₂ = N B A ₂ . ₂ = 50 0.200 (0.02)^2 60^ = 0.004 0.5 = 0.002 Wb The magnitude of the average induced emf is given by Faraday's law of induction: e = | t | = | ₂ - ₁ t | Substituting t = 0.100 s : e = | 0.002 - 0.004 0.100 | = 0.002 0.100 = 0.02 V Using = 3.14 , we