A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are $F_{1} {,F}_{2} {and F}_{3}$ respectively and are in the plane of the paper and along the direction shown, the force on the segment QP is

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

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

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

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

answer is B.

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Detailed Solution

The FBD of the loop is as shown

Therefore, force on QP will be equal and opposite to sun of forces on other sides.

Thus, $F_{QP} = \sqrt{{(F_{3} - F_{1})}^{2} + F_{2}^{2}}$

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