Magnetic flux and induced emf

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Question

If the rod is moving with a constant velocity of 12 cm /s then the power (in watt) that must be supplied by an external force in maintaining the speed is $p m W$ . Find the value of $p$ .
$(Given B = 0.5 Tesla, l = 15 cm, v = 12 cm / s, Resistance of rod R_{AB} = 9.0 mΩ)$

Moderate

Solution

$\begin{array}{l} E = B v l \\ i = \frac{E}{R} = \frac{B v l}{R} \\ P = i E = \frac{B v l}{R} \times B v l \\ \Rightarrow P = \frac{B^{2} v^{2} l^{2}}{R} = \frac{0.5 \times 0.5 \times 0.12 \times 0.12 \times 0.15 \times 0.15}{9 \times 10^{- 3}} = 9 \times 10^{- 3} W \end{array}$

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The diagram shows a circuit having a coil of resistance $R = 2.5 Ω$ and inductance L connected to a conducting rod PQ which can slide on a perfectly conducting circular ring of radius 10 cm with its centre at 'P'. Assume that friction and gravity are absent and a constant uniform magnetic field of 5 T exists as shown in figure.

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