Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• The cyclotron is a device for accelerating protons (or other charged particles) to high energies. The protons are held in a circular orbit of radius R = p/eB by a uniform magnetic field B. Twice in each orbit they are subjected to an accelerating electric field. As they speed up, R increases and they spiral slowly outward. (a) Show that the period of each orbit is T = 2πγm/(eB). (b) As long as the motion is nonrelativistic, γ ≈ 1 and the period is constant. This greatly simplifies the design of the cyclotron, since the accelerating field can be applied at a constant frequency. Assuming that a cyclotron can tolerate no more than a 2% increase in the period, what is the highest kinetic energy of the protons it can produce?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.