A circular coil of radius 10 cm, 100 turns and resistance 2 $Ω$ is placed with its plane perpendicular to horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. The induced current through the coil is (Horizontal component of earth’s magnetic field is $3.0 \times 10^{- 5} T$ )

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75.4 × 10^–4 A

75.4 × 10^–5 A

3.77 × 10^–4 A

37.7 × 10^–4 A

answer is A.

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Detailed Solution

$\begin{array}{l} I = - \frac{NBA (\cos θ_{2} - \cos θ_{1})}{Δt} \\ = - \frac{100 \times 3 \times 10^{- 5} \times π \times 10^{- 2} \times (- 1 - 1)}{2 \times 0.25} \\ = 3.77 \times 10^{- 4} A \end{array}$

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