A circular coil of 50 turns and cross-sectional area 2 m ^2 is placed such that its plane is perpendicular to a time-varying magnetic field. The magnetic field changes with time according to the relation B(t) = 0.2t^2 - 0.05t (where B is in tesla and t is in seconds). The magnitude of the induced emf in the coil at t = 2 s will be:

Step-by-step solution

The magnetic flux linked with the coil is given by = NBA . Since the plane of the coil is perpendicular to the magnetic field, the angle between the area vector and the magnetic field is = 0^ . Thus, (0^ ) = 1 . Substituting the given values: (t) = 50 2 (0.2t^2 - 0.05t) (t) = 100(0.2t^2 - 0.05t) = 20t^2 - 5t According to Faraday's law, the magnitude of the induced emf is |e| = d dt . Differentiating the flux equation with respect to time: |e| = d dt (20t^2 - 5t) = 40t - 5 At t = 2 s , the magnitude of the induced e