Aconstant current i circulates counterclockwise around a wire loop in the shape of a triangle, lying in x-y plane, with vertices at the points (0, 0, 0), (a, 0, 0), and (0,a,0). show that the total force on the loop is zero in the presence of a constant magnetic field b = bo(z).

Considering a triangle like the one of the figures, you can obtain the total magnetic force applied on it like the addition of the forces applied to each of the 3 sides.

Been the magnetic force formula:

For each segment:

Segment 1 (from [0,0,0] to [a,0,0]):

Segment 2 (from [a,0,0] to [0,a,0]):

Segment 3 (From [0,a,0] to [0,0,0]):

Total force on the wire loop:

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get