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. $\sqrt{(F_3-F_1)^2-F_2^2}$
• B. $F_3-F_1+F_2$
• C. $F_3-F_1-F_2$
• D. $\sqrt{(F_3-F_1)^2+F_2^2}$

Answer 1

Answer: (D)

$\sqrt{(F_3-F_1)^2+F_2^2}$

Answer 2

$F_4 \sin \theta =F_2$
$F_4 \cos \theta =(F_3-F_1)$
$\therefore F_4=\sqrt{(F_3-F_1)^2+F_2^2}$
For a closed loop there is no translation.