The magnetic flux linked with a coil, in weber, is given by the equation : $\mathrm{\varphi }=5{\mathrm{t}}^2+3\mathrm{t}+16$ . The induced e.m.f. in the coil at t=4 s will be 
 

Given data: equation - $\varphi =5t^2+3t+16$

Concept used: magnetic flux

Detailed solution:

A measurement of the total magnetic field that traverses a specific area is magnetic flux.

  $\Phi =5t^2+3t+16$

  $\left|\text{e}\right|=\frac{\text{d}\varphi }{\text{dt}}$ 

  $=\frac{\text{d}}{\text{dt}}\left[5{\text{t}}^2+3\text{t}+16\right]$

  $\text{=10 t+3}$

 $|e{|}_{t=4}=10(4)+3=43 \text{V}$ 

 $e=-43\text{ Volts }$