Solve the problems:
The Mathematical Methods in Physical Sciences
Q1. The operating equation for a synchrotron in the relativistic range is
qB = wm[1 - (wR)^2/c^2]^1/2
Where q and m are the charge and rest mass of the particle being accelerated, B is the magentic field strength, R is the orbit radius, q is the angular frequency, and c is the speed of light. If w and B are varied (all other quantities constant), show that the relation between dw and dB can be written as
dB/B^3 = (q/m)^2 dw/w^3
or as dB/B = dw/w [1 - (wR/c)^2]^-1
Q2. If w = the integral of (ax + by), show that b dw/dx - a dw/dy = 0.
Hint: Let ax + by = z.