Do magnetic forces obey Newton's third law. Verify for two current elements `dvecl_1=dlhati` located at the origin and `dvecl_2=dlhatj` located at (0, R, 0). Both carry current I.

Explanation

In Biot-savart's law, magnetic field B is parallel (II) to `idlxxr` and idl have its direction along the direction of flow of current.
Here. For the direction of magnetic field At `dl_(2)`, located at (0,R,0) due to wire `d_(1)` is given by `B||idlxxr` or `hatixxhatj` (because poiint (0,R,0) lies on y-axis), but `hatixxhatj=hatk`
So, the direction of magnetic field at `d_(2)` is along z-direction.
The direction of magnetic force exerted at `d_(2)` because of the first wire along the x-axis `F=i(IxxB)` i.e., `F||(ixxk)` or along `-hatj` direction.
Therefore, force due to `dl_(1)` on `dl_(2)` is non-zero.
Now, for the direction of magnetic field At `d_(1)`, located at (0,0,0) due to wire `d_(2)` is given by `B||idlxxr` or `hatjxx-hatj` (because origiin lies on y-direction w.r.t. point (0,R,0), but `jxx-hatj=0`
So, the magnetic field at `d_(1)` does not exist.
Force due to `dl_(2)` on `dl_(1)` is zero.
So, magnetic forces do not obey newton's third law.