The magnetic flux passing through a stationary square coil is given by the expression = 2t^3 - 3t^2 - 12t + 8 Wb , where t is the time in seconds. At what time will the induced electromotive force (emf) in the coil be zero?

Step-by-step solution

The magnetic flux is given by = 2t^3 - 3t^2 - 12t + 8 According to Faraday's law of electromagnetic induction, the induced emf is given by e = - d dt Differentiating the given expression with respect to time t e = - d dt (2t^3 - 3t^2 - 12t + 8) e = -(6t^2 - 6t - 12) For the induced emf to be zero, e = 0 6t^2 - 6t - 12 = 0 t^2 - t - 2 = 0 (t - 2)(t + 1) = 0 Since time cannot be negative, t = 2 s Answer: 2 s