Chapter 6.3, Problem 18P

Two moving charged particles exert forces on each other because each one creates a magnetic field in which the other moves (see Problem 4.6). These two forces are proportional to and where $r$ is the vector joining the particles. By using ( 3.9), show that these forces are equal and opposite (Newton’s third "law") if and only if $r\times \left(v_1\times v_2\right)=0.$ Compare Problem 14.