Self-inductance of a coil is 2mH, current through this coil is, `I=t^(2)e^(-t)` (t = time). After how much time will the induced emf be zero?

Explanation

Induced emf, `E=-L(dI)/(dt)`
Now, `(dI)/(dt)=(d)/(dt)(t^(2)e^-t)=2te^(-t)-t^(2)e^(-t)`
`=-e^(-t).t(t-2)`
Hence, `E=Le^(-t)t(t-2)`
So, if E = 0, then t = 0 or 2
Therefore, after 2s from the initial moment, the induced emf will be zero.