How to derive kinetic energy equation for charged particles

[Proz3m0]

I know there are some threads discussing about the Lorentz force equation but this is something different I came across and I couldn't find anyway to derive that formula.

To be specific I'm talking about a charged particles in a magnetic field, where F=vqB and everything that is moving has kinetic energy, later on I was shown that kinetic energy 1/2mv² = q²B²R² / 2m

Can anyone show me how that new formula is derived?

 

[blue_leaf77]

Welcome in Physics Forum!
For threads posted under the Homework section, the post is recommended to follow the given template, in addition the OP should also show some initial effort in solving his/her own problem. For instance the template asks the OP to write down any related formula, besides F=qvB what other equation do you have for a charged particle moving under a magnetic field? Hint: consider the nature of the magnetic Lorentz force.

 

[Noctisdark]

Imagine a happy charged particle wizzing around when, all of a sudden, it enters a magnetic field, and here when the lorentz force come in F = q (v x B) and the field exert a force on the particle that is orthogonal to it's velocity one thing you can predict is that the particle will rotate (will prove it if you want,but not now) and when an object rotate there is some force forcing it to stay in orbit that is the lorentz force (a centripetal force), Good luck !