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An alternating electric field, of frequency \( v \), is applied across the dees (radius = R) of a cyclotron that is being used
\( \mathrm{P} \) to accelerate protons (mass \( =\mathrm{m} \) ). The operating magnetic

W. field (B) used in the cyclotron and the kinetic energy \( (K) \) of the proton beam, produced by it, are given by: \( \quad \) (2012 Pre)
(a) \( \mathrm{B}=\frac{\mathrm{m} v}{\mathrm{e}} \) and \( \mathrm{K}=2 \mathrm{~m} \pi^{2} v^{2} \mathrm{R}^{2} \)
(b) \( \mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}} \) and \( \mathrm{K}=\mathrm{m}^{2} \pi v^{2} \mathrm{R}^{2} \)
(c) \( B=\frac{2 \pi m v}{e} \) and \( K=2 m \pi^{2} v^{2} R^{2} \)
(d) \( \mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}} \) and \( \mathrm{K}=\mathrm{m}^{2} \pi v \mathrm{R}^{2} \)
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