The magnetic flux linked with a coil satisfies the relation = (4 t^2+6 t+9 ) Wb , where t is time in second. The emf induced in the coil at t=2 ~s is

Step-by-step solution

The induced electromotive force (emf) in a coil is given by Faraday's law of induction, which states that the magnitude of the induced emf is equal to the rate of change of magnetic flux through the coil: | | = | d dt | Given the magnetic flux = 4t^2 + 6t + 9 , we differentiate this expression with respect to time t : d dt = d dt (4t^2 + 6t + 9) d dt = 8t + 6 To find the induced emf at t = 2 s, we substitute t = 2 into the expression for the rate of change of flux: = 8(2) + 6 = 16 + 6 = 22 V Answer: 22 V