Question

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 directions shown, the force on the segment $QP$ is

• A. $\sqrt{\left(F_{3} - F_{1}\right)^{2} - F_{2}^{2}}$
• B. $F_{3}- \, F_{1}+F_{2}$
• C. $F_{3}- \, F_{1}- \, F_{2}$
• D. $\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}$

Answer 1

Answer: (D)

$\because $ Net force on current carrying closed loop is zero
$\therefore F_{P Q}=\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}$