I have a very simple question
I'm working on a small project, and I worked out sometime that I can't seem to verify online
Basically, I'm trying to find how the magnetic field strength inside a synchrotron has to increase as a function of the velocity of the particles. I understand that there are other things going on in synchrotrons, but I'm really looking at the basics for the sake of this project
My thoughts go as follows:
Since the Centripetal force required to keep the particles in a ring of constant radius is Fc=m.v^2/r
and that the magnetic force applied on a particle by a magnetic field perpendicular to its velocity is FB = V.B
Then we would need the strength of the magnetic field proportionally to the first power of the velocity. This way the product V.B would increase proportionally to the square of the velocity, as we wanted originally
Is all of this correct?
If there's something i'm missing, can you tell me what that is?
Thank you so much