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

Answer

D

Explanation

Since all the given forces are lying in plane, so the given loop is in equilibrium
`F_(4) = F_(4) cos phi = F_(2)`
`F_(4) = F_(4) sin phi = F_(3) - F_(1)`
`implies F_(4)^(2) = F_(2)^(2) + (F_(3) - F_(1))^(2) F_(4) = F_(2)`
`implies F_(4) = sqrt(F_(2)^(2) + (F_(3) - F_(1))^(2))`