An alternating electric field, of frequency $v$, is applied across the does (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

Question

$B = {{m\upsilon } \over e}$ and $K = 2m{\pi ^2}{\upsilon ^2}{R^2}$

$B = {{2\pi m\upsilon } \over e}$ $K = {m^2}\pi \upsilon {R^2}$

$B = {{2\pi m\upsilon } \over e}$ $K = 2m{\pi ^2}{v^2}{R^2}$

$B = {{m\upsilon } \over e}$ $K = {m^2}\pi \upsilon {R^2}$

Solution

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