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 F1, F2, and F3 respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

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 F1, F2, and F3 respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is (A) √(F3-F1)2-F22 (B) F3-F1+F2 (C) F3-F1-F2 (D) √(F3-F1)2+F22

Tardigrade Admin · Accepted Answer

F4 sin θ =F2 F4 cos θ =(F3-F1) ∴ F4=√(F3-F1)2+F22 For a closed loop there is no translation.

Q. 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

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

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

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

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

$F_{4} sin θ = F_{2}$
$F_{4} cos θ = (F_{3} - F_{1})$
$∴ F_{4} = (F_{3} - F_{1})^{2} + F_{2}^{2}$
For a closed loop there is no translation.

Q. 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 F1​,F2​, and F3​ respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

(F3​−F1​)2−F22​​

F3​−F1​+F2​

F3​−F1​−F2​

(F3​−F1​)2+F22​​