A square loop of area 25 cm² has a resistance of 10 Ω. The loop is… | MHT CET 2024 (4 May, Shift 1)

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Motional EMF

A square loop of area $25\text{ cm}^{2}$ has a resistance of $10\ \Omega$ . The loop is placed in uniform magnetic field of magnitude 40 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be

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Answer: (b)

Side $L = \sqrt{25\text{ cm}^2} = 5\text{ cm} = 0.05\text{ m}$ ; pulled out in 1 s, so $v = 0.05\text{ m/s}$ .
$e = BLv = 40 \times 0.05 \times 0.05 = 0.1\text{ V}$
$P = \dfrac{e^2}{R} = \dfrac{0.01}{10} = 10^{-3}\text{ W}$
$W = Pt = 10^{-3} \times 1 = 1.0 \times 10^{-3}\text{ J}$
So the answer is (b) $1.0 \times 10^{-3}\text{ J}$ .

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