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Do magnetic forces obey Newton's third l...

Do magnetic forces obey Newton's third law. Verify for two current elements `vec(dl_(1))=dl(hati)` located at the origin and `vec(dl_(2))=dl(hatj)` located at (0, R, 0). Both carry current I.

Text Solution

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1. According to Biot-Savart law, direction of magnetic field is in the direction of `Ivec(dl)`.
2. Magnetic field for `dl_(2)`, element at (0, R, 0) is given by,
`vecB=Ivec(dl_(2))xxvecr`
= `Idl(hati)xxrhatj`
= `Idlr(hatixxhatj)`
`thereforevecB=Idlr(hatk)`
That means, it is in z-direction.
3. Force on this element,
`vecF_(2)=Ivec(dl_(2))xxvecB`
= `Idl(hati)xxB(hatk)`
= `IdlB(hatixxhatk)`
= `IdlB(-hatj)`
This force is in y-direction.

4. Magnetic force on `dl_(1)` element at origin,
`Ivec(dl_(1))xxvecr=Idlhatjxxr(-hatj)`
= 0
`vecr=r(-hatj)` because first element is at (0, R, 0) with respect to that this element is in y-direction. So, magnetic field is zero at this point. So, magnetic force on `vec(dl_(1))` due to `vec(dl_(2))` be zero.
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