The figure below represents the one vertex of square loop at origin,
For wire
AB , magnetic filed,
B0(1+0)=B0 x=0 For wire CD, magnetic filed,
B0(1+) x=L For wire
BC, magnetic filed,
B0(1+) y=L For wire AD, magnetic filed,
B0 y=0 The forces in the square loop,
F1=IB0=IB0L F2=IB0(1+)dx=IB0L F3=IB0(1+)dx=IB0L F4=IB0dx=IB0L The force in
x direction,
Fx=F3−F1 Fx=IB0L−IB0L Fx=IB0L Similarly, The force in y direction,
Fy=F2−F4 Fy=IB0L−IB0L Fy=IB0L The net magnitude of force,
F=√(IB0L)2+(IB0L)2 F=