Question

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The three above equations need to be shown and can i please have an explanation as well?

Answer 1

i) We know that when the magnetic field is acting on a charged particles, then it gives rise to Lorentz force: - vector F = f (vector v times vector B)/c. (In eq^n 1, we have divided by c as we are working in CGS units. For SI units F = f (V times B)). Therefore F = f v/c B sin theta thatis (2) Here, the magnetic field is perpendicular to velocity of electron (for synchrotron b direction is perpendicular to the plane of motion of e^-). F = f v B/C thatis (3) the Lorentz force the necessary centripetal force as rightarrow f v B/c = mv^2 /R or mv = Bf R/C (p = mv = momentum) or r = pc/Bf for electron f = e R = pc/Be thatis (4) (ii) At relativistic speed we can take velocity of e^- TideEqual C. so, the time period is T = 2 pi R/C = Circumference length/velocity and the Angular frequency for rotation is