Question

We have seen that in case of parallel conducting wires carrying steady currents, the Biot-Savart law and the Lorentz force law give the result in Eq. (10.44 A):

\[\ce{F_{21} = -F_{12}}\]

Is this consistent with Newton's third law? (Consider for example the gravitational pull experienced by the Earth towards the Sun and that by the Sun towards the Earth.)

Answer 1

Yes, this is consistent with Newton’s third law. For two parallel current-carrying wires,

\[\ce{F_{21} = -F_{12}}\]

This means that the force exerted by wire 1 on wire 2 is equal in magnitude and opposite in direction to the force exerted by wire 2 on wire 1. This is similar to the gravitational interaction between the Sun and the Earth: the Earth pulls the Sun with the same magnitude of force with which the Sun pulls the Earth, but in the opposite direction.

Hence, the magnetic forces between the two parallel wires form an action-reaction pair and obey Newton’s third law.