A particle with a charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a path of radius R, find expressions for (a) its speed and (b) its mass.
K=1/2mv^2 and R=mv/qB
The Attempt at a Solution
I couldn't think of anything to do besides solve for v and m in the second equation. I figured this couldn't be correct because that's trivial. Since this is somewhat recreational work for me, I shortly gave up and consulted a solution. The solution I found showed the method for solving the problem to be dividing K by R and then solve for v. This is then substituted into the second equation to answer the second question.
I NEVER would have made this intuitive leap so I'm glad I didn't waste too much time on it. However, even after checking the solution, I'm confused about how or why that approach would be taken at all. Is this something that someone could explain to me?