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An alternating electric field, of frequency ν, is applied across the dees (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:
- B = mv/e and K = 2mπ²ν²R²
- B = e/2mπν and K = mπ²νR²
- B = e/2mπν and K = 2mπ²ν²R²
- B = mv/e and K = mπ²νR²
Correct answer: B = e/2mπν and K = 2mπ²ν²R²
Solution
In a cyclotron, the magnetic field (B) is related to the frequency (ν) by B = e/2mπν, and the kinetic energy (K) of the accelerated particle is given by K = 2mπ²ν²R². These relations are derived from the principles of circular motion and energy in a cyclotron.
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