# Can magnetic forces do work on a moving, radiating charged particle?

I am not sure if this a repeat. Also, I am a high school student, so I'm saying this from what I understood of my teacher's explanation of Maxwell's law.

Imagine a particle moving in a magnetic field. It will execute circular motion. But as it is accelerating, Maxwell says that it should radiate EM waves. If it is emitting EM waves, shouldn't it lose energy? If it does, it should lose velocity, right? And isn't the magnetic field applying a force $$B$$ on it?

So won't $$W=B\cdot S$$?

As $$v$$ isn't constant, $$dx/dt$$ isn't constant, so work should be done, right?

And so isn't the magnetic field here doing work?

• And isn't the magnetic field applying a force 𝐵 on it? $\vec B$ is the symbol for the magnetic field. A magnetic field is not a force. The force it exerts is $\vec F = q \vec v \times \vec B$. Sep 17, 2022 at 17:23
• Yea sorry my bad but consider qv×b as force B for this one Sep 18, 2022 at 2:50
• Since you specified that $\vec{B}$ (and $\vec{E}$) are constant, there should be no radiation.
– Bio
Sep 18, 2022 at 4:49

No, the force from the magnetic field is not equal to $$\vec B$$, it is $$\vec F= q \vec v \times \vec B$$. So $$\vec F$$ is perpendicular to $$\vec v$$, and a force that is perpendicular to the velocity does no work since the dot product $$dW=\vec F \cdot d\vec x=0$$.