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In Fig., a semicircular wire is placed i...

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.

Text Solution

Verified by Experts

The wire is equivalent to the figure shown below.

`:' theta =0`, therefore `F_(res)=0`
Forces on individual parts are marked in Fig. by `ox` and `odot`
By symmetry, there will be pair of forces forming couples.

`tau=int_0^(pi//2) i(Rd theta)B sin (90- theta)2 R cos theta`
`=(ipiR^2)/2B` or `vectau=(-hatj)=(ipiR^2)/2 B(-hatj)`.
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