A conducting rod of length l is moved at constant velocity $v_{0}$ on two parallel conducting, smooth, fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane of the rails as shown in figure. A resistance R is connected between the two ends of the rail. Then which of the following is/are correct

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Lenz’s law is not satisfied for direction of current in Loop

If resistance R is doubled then power required to maintain the constant velocity

v_{0}

becomes half

If applied external force is doubled then a part of external power increases the velocity of rod

The thermal power dissipated in the resistor is equal to rate of work done by external person pulling the rod

answer is A, B, D.

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Detailed Solution

Rate of workdone by external agent is

\frac{dw}{dt} = \frac{B i Ld x}{dt} = B i l V

and thermal power dissipated in the resistor = (BVl)I clearly both are equal.

If applied external force is doubled the rod will experience a net force and hence acceleration as a result velocity increases $I = \frac{e}{R}$ on doubting ‘R’ current and hence required power becomes half P = BilV

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