The loop ABCD is moving with velocity ‘v’ towards right. The magnetic field is 4T. The loop is connected to a resistance of 8 $Ω$ . If steady current of 2A flows in the loop then value of ‘v’ if loop has a resistance of 4 $Ω$ , is $v = \frac{100}{x} m / s$ where $x$ is_________(Given AB=30cm, AD=30cm)

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Detailed Solution

The induced emf in the loop is $e = Blve = B (AD) \sin 37^{0} v = 4 \times 0.3 \sin 37^{\circ} v$

Effective resistance of the circuit is $R = (4 + 8) = 12 Ω$ ; Hence $i = \frac{e}{R} = \frac{Blv}{R}$

$\Rightarrow 2 = \frac{4 \times 0.3 \times \sin 37^{0} v}{(4 + 8)}; ∵ v = \frac{100}{3} m / s$

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