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 . [2023]

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Solution

Q.
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 $π = \frac{22}{7}$ ) [2023]

Ans.
(44)

$B_{due to solenoid} = μ_{0} n I$

$ϕ_{through square} = μ_{0} n I \times A (A = Area)$

$EMF = μ_{0} n A \times \frac{d I}{d t} = μ_{0} n A \times I_{0} ω \cos ω t$

$EMF amplitude = μ_{0} n A \times I_{0} ω$

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

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

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