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

Answer

a

Explanation

Net force on loop is zero.

`F_(4) sin theta = F_(2)`
` F_(4) cos theta = F_(3) - F_(1)`
Squaring on both sides and then adding , we get :
`F_(4) = sqrt((F_(3) - F_(1))^(2) + F_(2)^(2))`