Newton's Third Law applies in weak form primarily in contexts involving electromagnetic forces, particularly when analyzing the interactions between moving charges. In the case of two identical charges moving along the x and y axes, the electrical forces are repulsive, while the magnetic forces generated do not act as equal and opposite, yet momentum is conserved due to the momentum carried by the fields themselves. For a deeper understanding, consulting resources such as Griffiths' textbooks on electrodynamics is recommended.
PREREQUISITESPhysics students, educators, and researchers interested in advanced mechanics and electromagnetic theory will benefit from this discussion.
Consider two identical charges moving along the x and y axes with same speed away from the origin. The electrical forces between them is repulsive, but now just find out how the magnetic forces between them behave. You don't have to calculate -- just roughly think of the charges as currents and find the direction of the associated magnetic fields like we do for currents.
The total force of one on the other is equal to the force of the other on the former, but they are not opposite.
Ultimately, momentum will be conserved, because the fields themselves carry momentum.