We know that Ampere’s force per unit length on a wire element in a magnetic field is given by.
is the unit vector along the direction of current. (1)
Now, let us take an element of the conductor i2 , as shown in the figure. This wire element is in the magnetic field, produced by the current i1 , which is directed normally into the sheet of the paper and its magnitude is given by,
From Eqs. (1) and (2)
Then according to the Newton’s third law the magnitude of sought magnetic interaction force