The flux of a magnetic field through a closed conducting loop varies with time according to the relation = at^2 + bt + c . Given that the magnitudes of a , b , and c are 0.20 , 0.40 , and 0.60 respectively in SI units, compute the induced emf at t = 2 s .

Step-by-step solution

The magnetic flux through the loop is given by = at^2 + bt + c . According to Faraday's law of electromagnetic induction, the magnitude of the induced emf is given by: |e| = | d dt | Differentiating the given expression for flux with respect to time t : d dt = d dt (at^2 + bt + c) = 2at + b Substituting the given values a = 0.20 , b = 0.40 , and t = 2 s : |e| = 2(0.20)(2) + 0.40 |e| = 0.80 + 0.40 = 1.2 V