The magnetic flux through a loop varies according to the relation Φ = 8t^{2} + 6t + C, where ‘C’ is constant, 'Φ' is in milliweber and 't' is in second. What is the magnitude of induced e.m.f. in the loop at t = 2 seconds.

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#### Solution

Magnetic flux through the coil is given by relation

Φ = 8t^{2} + 6t + c (where c is constant) (i)

To find the magnitude of the induced e.m.f. ‘e’ in the loop at t = 2 seconds, we know that `e=|(dphi)/dt|`

Differentiating equation (i) w.r.t. t we get,

e = 16t + 6

e = 16 × (2) + 6

e = 38 millivolt = 0.038 volt

Hence, the magnitude of induced e.m.f. is 0.038 volt.

Concept: Electromagnetic Induction

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