Prove that the force acting on a current carrying wire, joining two fixed points a and b in a uniform magnetic field, is independent of the shape of the wire.

Magnetic force acting on a current carrying wire in an uniform magnetic field is given by

where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l

Since

is vector

Also, the length of the wire is fixed from A to B, so force is independent of the shape of the wire.