Given-

Current passing through the wire = I A

The wire is kept in the x−y plane along the curve,

Also given that the magnetic field exists in the z direction.

To find the magnetic force on the portion of the wire between x = 0 and x = λ.

We know ,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

For a differential length dl,

The effective force on the whole wire due to force acting on the wire of length λ placed along the x axis.

So,