A rectangular loop of resistance R=5 is placed in a uniform magnetic field such that the magnetic flux through the loop increases according to the relation =4 t^2-2 t where is in weber and t is in second. The current induced at t=3 second is:

Step-by-step solution

The magnetic flux through the loop is given by = 4t^2 - 2t . According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) is given by the negative rate of change of magnetic flux: = - d dt Differentiating with respect to t : d dt = d dt (4t^2 - 2t) = 8t - 2 Thus, the magnitude of the induced emf is | | = |8t - 2| . The induced current I is given by Ohm's law, I = | | R , where R = 5 . At t = 3 seconds: | | = 8(3) - 2 = 24 - 2 = 22 V I = 22 5 = 4.4 A Answer: 4.4 A