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 `because theta=0`
`because F_(res)=0`
forces on individual parts are marked in the figure by `ox` and `odot` . By symmetry their will be pair of forces forming couples.
`tau=underset(0)overset(pi//2)inti(Rd theta)Bsin(90-theta).2Rcostheta`

`tau=(ipiR^(2))/(2)B`
`impliesvectau=(ipiR^(2))/(2)B(-hatj)`