A closed loop `PQRS` carrying a current is place in a unifrom 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

Options

A. `F_3 - F_1 + F_2`
B. `F_3 - F_1 - F_2`
C. `sqrt((F_3 - F_1)^2 + F_2^2)`
D. `sqrt( (F_3 - F_1)^2 - F_2^2) `

Answer

C

Explanation

Net force on closed loop is zero
`vecF_1 + vecF_2 + vecF_3 + vecF_4 = 0`
`rArr |vecF_4| = |vecF_1 + vecF_2 + vecF_3 |`
` rArr F_4 = sqrt( (F_3 - F_1)^2 + F_2^2)`