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Q.

A uniform magnetic field $B = 0.5 T$ exists in a circular region of radius $R = 5 m$ . A loop of radius $R = 5$ m encloses the magnetic field at $t = 0$ and then pulled at uniform speed $v = 2 m s^{- 1}$ in the plane of the paper. Find the induced emf (in V) in the loop at time $t = 3 s$ .

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answer is 8.

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Detailed Solution

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$I n Δ O_{1} M P O_{1} M = (V t - R) + \frac{1}{2} (2 R - V t) O_{1} M = \frac{1}{2} V t P M = \sqrt{R^{2} - O, M^{2}} P M = \sqrt{\frac{4 R^{2} - V^{2} t^{2}}{4}} P N = 2 P M = \sqrt{4 R^{2} - V^{2} t^{2}} ε = B V l ε = B V \sqrt{4 R^{2} - V^{2} t^{2}} ε = 8 V$

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