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Question

A conducting rod of length is moved at constant velocity V0 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 :


A

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

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B

If applied external force is suddenly doubled then the velocity of rod will instantly double.

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C

If applied external force is suddenly doubled then the velocity of rod will instantly quadruple.

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D

If resistance R is doubled then power required to maintain the constant velocity V0 becomes half.

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Solution

The correct options are
A

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


D

If resistance R is doubled then power required to maintain the constant velocity V0 becomes half.


Rate of work done by external agent is :
dWdt=BIL.dxdt=BILv and thermal power dissipated in resistor = eI = (BeL)I

Clearly both are equal, hence (A)
If applied external force is doubled, the rod will experience a net force and hence acceleration. As a result velocity increases, Since ; I=eR ; On doubling R current and hence required power become half. since, P = BILv


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