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. `sqrt((F_(3) - F_(1))^(2) + F_(2)^(2))`
C. `sqrt((F_(3) - F_(1))^(2) - F_(2)^(2)`
D. `F_(3) - F_(1) + F_(2)`

Answer

B

Explanation

The `FBD` of the loop is as shwon

Therefore, force on `QP` will be equal and opposite to sum of forces on other sides,
Thus, `F_(QP) = sqrt((F_(3) - F_(1))^(2) + F_(2)^(2))`