The magnetic flux through a loop is varying according to relation `phi=6t^(2)+7t+1` where `phi` is in milliweber and t is in second. What is the e.m.f. induced in the loop at t = 2 second ?

Explanation

Data t=2s, `Phi= 8t^(2) + 6t +C`, where C is a numerical constant and `Phi` is in milliweber (mWb)
The magnetic of the induced emf, `E=|(dPhi)/(dt)|`
`therefore E=d/(dt)(8t^(2) + 6t +C) = 16t + 6=0`
`=(16 xx 2) + 6 = 32 + 6 = 38 "mV " 38 xx 10^(-3) V`