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  4. The magnetic flux linked with a coil satisfies the relation φ= (4t2 + 6t + 9) Wb, where t is the time in second. The e.m.f. induced in the coil at t = 2 second is

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Q. The magnetic flux linked with a coil satisfies the relation $\phi= (4t^2 + 6t + 9) Wb$, where $t$ is the time in second. The e.m.f. induced in the coil at $t\, =\, 2$ second is

WBJEEWBJEE 2012Electromagnetic Induction

Solution:

Given $\phi=4 t^{2}+6 t+9$ and $t=2\, s$
We know that $\varepsilon=\frac{d \phi}{d t}$
Here, $\frac{d \phi}{d t}=8 t+6$
$\left(\frac{d \phi}{d t}\right)_{t=2} =8 \times 2+6$
$\varepsilon =22\, V$