In Fig., a semicircular wire is placed in a uniform field `vec B` directed towards right. Find the resultant magnetic force and torque on it.

Explanation

The wire is equivalent to
`:. 0=0`
`:. F_(res)=0`
forces on individual parts are marked in the figure by `ox` and `o.` By symmetry their will be pair of forces forming couples.
`tauunderset(0)overset(pi//2)inti(Rd theta)B sin (90-theta).2Rcos theta`
`=tau(ipiR^(2))/2B`
`rArr tau(ipiR^(2))/2B(-hatj)`