A closed loop $P Q R S$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment $P S$ , $S R$ and $R Q$ are $F_{1}$ , $F_{2}$ and $F_{3}$ respectively and are in the plane of the paper and along the directions shown, the force on the segment $Q P$ is

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$\sqrt{{(F_{3} - F_{1})}^{2} + F_{2}^{2}}$

$\sqrt{{(F_{3} - F_{1})}^{2} - F_{2}^{2}}$

$F_{3} + F_{1} - F_{2}$

$F_{3} - F_{1} + F_{2}$

answer is D.

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Detailed Solution

If $F_{4}$ is the force on segment $Q P$ , then

$\vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}} + \vec{F_{4}} = 0$

and $\vec{F_{4}} = - (\vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}})$

or $F_{4} = \sqrt{{(F_{3} - F_{1})}^{2} + F_{2}^{2}}$

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