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An equilateral triangle frame $P Q R$ of mass $M$ and side $a$ is kept under the influence of magnetic force due to inward perpendicular magnetic field $B$ and gravitational field as shown in the figure. The magnitude and direction of current in the frame so that the frame remains at rest, is
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$I = \frac{2 M g}{a B}$ ;anti-clockwise

$I = \frac{2 M g}{a B}$ ;clockwise

$I = \frac{M g}{a B}$ ;anti-clockwise

$I = \frac{M g}{a B}$ ;clockwise

answer is B.

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Detailed Solution

$F_{MNPQ} = F_{MQ}$ and this force should be upwards to balance the weight.

$∴ i l B = m g,$ where

$l = M Q = \frac{a}{2}$

$∴ i (\frac{a}{2}) B = m g$

or $i = \frac{2 M g}{a B}$

Force is upwards if current is clockwise or current in $M Q$ is towards right.

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