Question

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

Answer 1

Given :

$\varphi =8t^2+6t+C$

where, $C$ is a constant, $t$ is in sec, $\varphi$ in milli-weber

The induced e.m.f. in the loop at $t=2$, on differentiating the equation with respect to '$t$'.

$\frac{d\varphi }{dt}=\frac{d}{dt}(8t^2+6t+C)$

$=16t+6$

at $t=2$

$\frac{d\varphi }{dt}=16\times \left(2\right)+6$

$=32+6$

$=38mWb/s$