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Q6.3 A long solenoid with $15$ turns per cm has a small loop of area $2.0 cm^{2}$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 A$ to $4.0 A$ in $0.1s$ , what is the induced emf in the loop while the current is changing?

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Given in a solenoid,

The number of turns per unit length is:

$n = 15turn/cm=1500turn/m$

loop area :

$A=2cm^2=2*10^{-4}m$

Current in the solenoid :

$initial current = I_{initial}=2$

$finalcurrent = I_{final}=4$

change in current :

$\Delta I$ $= 4-2 = 2$

change in time:

$\Delta t=0.1s$

Now, the induced emf:

$e=\frac{d\phi }{dt}=\frac{d(BA)}{dt}=\frac{d(\mu _0nIA)}{dt} = \mu _0nA\frac{dI}{dt}=\mu _0nA\frac{\Delta I}{\Delta t}$

$e=4\pi*10^{-7}*1500*2*10^{-4}*\frac{2}{0.1}=7.54*10^{-6}$

Hence, the induced emf in the loop is $7.54*10^{-6}$ .

Posted by

Pankaj Sanodiya

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