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

Answer 1

Answer: (D)

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