Lawrence's Insight "R cancels R"
- Last time we derived the radius of curvature of the trajectory of a charged particle in a constant magnetic field.
- E.O. Lawrence realized in 1929 an important feature of this equation which became the basis for his invention of the cyclotron.
R does indeed cancel R in above eqn. So What??
- The angular velocity is independent of R!!
- Therefore the time for one revolution is independent of the particle's energy! but bigger energy -> bigger radius that’s it!
- This fact can be exploited to provide the mechanism for acceleration of charge. The cyclotron….
- Rewrite in terms of angular velocity w !