# If I put charged particles in the center of long hollow cylinder shaped electromagnet, in a vacuum, would it accelerate them?

If I put charged particles in the center of long hollow cylinder shaped electromagnet, in a vacuum, would it accelerate them? Is this how particle accelerators work? If so are there formulas I could use to calculate the acceleration(my grandfather might be able to help me, he's an engineer)

• a traveling wave tube has a longitudinal static magnetic field generated by a solenoid, the electrons are accelerated by a static electric field. The magnetic field is there to keep them aligned with the axis, see en.wikipedia.org/wiki/Traveling-wave_tube – hyportnex May 6 '18 at 19:05

$$\vec{F}=q\vec{E}+q(\vec{v}\times\vec{B})$$
An electromagnet (under DC current)* does not produce any electric field, only a magnetic field, so the $q\vec{E}$ part is zero. Since $\vec{v}\times\vec{B}$ is always perpendicular to the velocity vector, by definition of the cross product, the magnitude of $\vec{v}$ cannot change. Therefore, a magnetic field can only bend the path of charged particles, not change their speed. If you want them to "accelerate" in the sense of a particle accelerator, you're much better off using an electric field (like the one generated between two charged parallel plates).