Magnetic flux and induced emf

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Question

Wire PQ with negligible resistance slides on the three rails with 5 cm/sec. If the current in 10 $Ω$ resistance when switch S is connected to position 1 is i₁ and when
the switch is at position 2 the current becomes i₂.Then the ratio i₁/i₂ is ____________.

Moderate

Solution

For position 1, Induced current
$i_{1} = \frac{e}{R} = \frac{B v l}{R}$
For position 2,Induced current
$i_{2} = \frac{e}{R} = \frac{B v (2 l)}{R}$
$\frac{i_{1}}{i_{2}} = \frac{\frac{B v l}{R}}{\frac{2 B v l}{R}} = \frac{1}{2}$

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Similar Questions

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.

At t = 0, the circuit is switched on and simultaneously a time varying external torque is applied on the rod so that it rotates about P with a constant angular velocity 40 rad/s. Find magnitude of this torque (in milli Nm) when current reaches half of its maximum value. Neglect the self-inductance of the loop formed by the circuit.

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