Question

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because,

• A. the two magnetic forces are equal and opposite, so they produce no net effect
• B. the magnetic forces do no work on each particle.
• C. the magnetic forces do equal and opposite (but non-zero) work on each particle
• D. the magenetic forces are necessarily negligible

Answer 1

The correct option is B the magnetic forces do no work on each particle.

The electric and magnetic forces are defined via the Lorentz force on a charged particle

$F=q(E+v\times B)$

The magnetic force comes from the second term which defines it to be perpendicular to the velocity and therefore displacement $dr$ so it doesn't do any work.