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The current generator i_g, shown in figure, sends a constant current i through the circuit. The wire ab has a length / and mass m, slide on the smooth, horizontal rails connected to i_g. The entire system lies in a vertical magnetic field B. The velocity of the wire as a function of time is

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$\frac{i l B t}{3 m}$

$\frac{2 i l B t}{m}$

$\frac{i l B t}{m}$

$\frac{i l B t}{2 m}$

answer is A.

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Detailed Solution

Force on the wire = ilB,

$∴ A c c e l e r a t i o n = \frac{i l B}{m}$

$∴ V e l o c i t y = \frac{i l B t}{m}$

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