A coil having 50 turns and an area of 0.1 m ^2 is placed in a uniform magnetic field. The plane of the coil makes an angle of 37^ with the direction of the magnetic field. The magnetic field varies with time according to the equation B = (2t^2 + t + 5) T . If the resistance of the coil is 15 , the induced current through the coil at t = 2 s will be:

Step-by-step solution

Angle between the magnetic field and the normal to the coil, = 90^ - 37^ = 53^ . Magnetic flux through the coil is given by: = NBA = 50 0.1 (2t^2 + t + 5) (53^ ) = 5 (2t^2 + t + 5) 3 5 = 3(2t^2 + t + 5) = 6t^2 + 3t + 15 Wb Magnitude of induced emf is: = | d dt | = d dt (6t^2 + 3t + 15) = 12t + 3 At t = 2 s , = 12(2) + 3 = 27 V Induced current, I = R = 27 15 = 1.8 A Answer: 1.8 A