# A magnetic flux passing perpendicular to plane of a coil is varying according to the relation. $\phi =3t^2+2t+5$ milliwebers. the emf induced at $t=2 \;sec$ is :

$(a)\;14\;mV \\ (b)\;14\;V \\(c)\;-14\;mV \\(d)\;31\;mV$

$\phi$ is in $mWb$
$E=\large\frac{-d \phi}{dt}$
$\qquad= \large\frac{-d}{dt}$$[3t^2+2t+5]$
$\qquad= -(6t+2)$
at $t=2 seconds$
$E= -(6 \times 2 +2)$
$\qquad= -14 \;mV$
Hence c is the correct answer.
answered Mar 21, 2014 by