MCQ
A square loop of side $2.0\,cm$ is placed inside a long solenoid that has $50$ turns per centimetre and carries a sinusoidally varying current of amplitude $2.5\,A$ and angular frequency $700\,rad\,s ^{-1}$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10^{-4} V$. The value of $x$ is $.........$(Take, $\pi=\frac{22}{7}$)
  • A
    $43$
  • B
    $42$
  • $44$
  • D
    $41$

Answer

Correct option: C.
$44$
c
$B _{\text {due to solenoid }}=\mu_0 nI$

$\Phi_{\text {through square }}=\mu_0 nI \times A \quad( A =\text { Area })$

$Emf =\mu_0 nA \times \frac{ dI }{ dt }$

$=\mu_0 n A \times I _0 \omega \cos \omega t$

$\text { Emf amplitude }=\mu_0 n A \times I _0 \omega$

$=4 \pi \times 10^{-7} \times \frac{50}{10^{-2}} \times 4 \times 10^{-4} \times 2.5 \times 700$

$=44 \times 10^{-4}\,V$

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