A loop, carring a current i, lying in the plane of the paper, is in the field of a long straight wire with current `i_0` (inward) as shown in Fig. Find the torque acting on the loop.

Explanation

The field due to current carrying wire is tangential to every point on the circular portion of the loop and hence the forces acting on these segments are zero.

Now consider two small elements of length `dr` at a distance `r` from the axis symmetrically as shown in figure. The magnitude of the force experienced by each element is `dF=B i dr=((mu_(0))/(2pi)(i_(0))/(r))i dr`
On element 1 it is into the page and on 2 it out of the page, `dtau=dFxx2r sin theta`
`=((mu_(0)i_(0)i)/(2pir)dr)`
Now total torque
`tau=(mu_(0)i_(0)i sin theta)/(pi)underset(a)overset(b)intdr=(mu_(0)i_(0)i)/(pi)sintheta(b-a)`