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  • A square loop of side is placed inside a long solenoid that has 50 turns per centimeter and carries a sin

A square loop of side 2.0\; cm is placed inside a long solenoid that has 50 turns per centimeter and carries a sinusoidally varying current of amplitude2.5\; 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})

Option: 1

44


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

emf induced in the solenoid \Rightarrow \mathrm{BA\omega N} \sin (\omega \mathrm{t}), \mathrm{\omega }=700 \mathrm{rad} / \mathrm{s}

\begin{aligned} & \text { Amplitude } \Rightarrow \mathrm{BA\omega N} \\ & \text { Area }(\mathrm{A})=2 \mathrm{~cm} \times 2 \mathrm{~cm} \\ & =4 \mathrm{~cm}^2 \\ & =4 \times 10^{-4} \mathrm{~m}^2 \\ & (\mathrm{~B})_{\text {solenoid }}=\mu_0 \mathrm{ni} \\ & =4 \pi \times 10^{-7} \times 5000 \times 2.5 \\ & =5 \pi \times 10^{-3} \\ & \mathrm{n}=\frac{50 \mathrm{turns}}{\mathrm{cm}}=\frac{5000}{\mathrm{~m}} \\ & \mathrm{i}=2.5 \end{aligned}Amplitude\; of\; emf =\left(5 \pi \times 10^{-3}\right)\left(4 \times 10^{-4}\right)(700)(1)$ $=5 \times \frac{22}{7} \times 4 \times 700 \times 10^{-7}=44 \times 10^{-4}

 

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