Q. A conducting ring of radius $0.4m$ is placed in a time varrying magnetic field $B=\left(2 + \frac{3 t^{2}}{\pi }\right)$ (where $B$ is in tesla and $t$ is in $s$ ) in such a way that its axis making an angle $60^\circ $ with magnetic field. The emf induced in the ring at $t=2s$ will be

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A

$0.48V$

B

$0.96V$

C

$0.36V$

D

$0.72V$

Solution:

$\phi=\overset{ \rightarrow }{B}\cdot \overset{ \rightarrow }{A}$
$=BAcos60^\circ $
$=\left(2 + \frac{3}{\pi } t^{2}\right)\pi \left(\right.0.4\left(\left.\right)^{2}\times \frac{1}{2}$
$=\left(2 + \frac{3}{\pi } t^{2}\right)\pi \times 0.08$
$\left|\right.E\left|\right.=-\left|\frac{d \phi}{d t}\right|$
$E=3\times 0.08\times 2t$
$E=3\times 2\times 2\times 0.08$
$=12\times 0.08$
$=.96V$

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