# Can magnetic field change kinetic energy?

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 not work on each particle

(c) the magnetic forces do equal and opposite (but non-zero) work on each particle

(d) the magnetic forces are necessarily negligible

## 2 Answers

Magnetic field does no work. The Lorentz force due to a point charge is $$\vec{F} = q(\vec{E}+\vec{v}\times\vec{B}).$$ The force due to the magnetic field is $$\vec{F}_{mag} = q(\vec{v}\times\vec{B}) .$$ The work done on $$q$$ due to the magnetic force per unit time is $$P_{mag} = \vec{F}_{mag}·\vec{v} = q(\vec{v}\times\vec{B})·\vec{v} = q(\vec{v}\times\vec{v})·\vec{B} = 0.$$ Thus, quite generally, forces due to magnetic fields do no work, because $$\vec{F}_{mag}$$ is orthogonal to $$\vec{v}$$.

• answer , given is b option ? shouldn't it be a option then ? – Aaliya Aug 8 at 11:08
• Not sure what you are asking. Magnetic forces do no work, B follows directly from this. – Puk Aug 8 at 18:24

It is because of b). Magnetic forces are vertical to the velocity and therefore do not do any work. They accelerate the particle but only change the direction and not the length of the velocity vector

• the answer given is b option , why ? – Aaliya Aug 8 at 11:07
• Because the magnetic field does not do any work. You changed your question. – Jan2103 Aug 8 at 11:13