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  • An alternating electric field, of frequency v, is applied across the dess (radius =R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in th

An alternating electric field, of frequency v, is applied across the dess (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:

Option: 1

B=\frac{m V}{e} \text { and } K=2 m \pi^2 V^2 R^2


Option: 2

B=\frac{2 \pi m V}{e} \text { and } R=m^2 \pi V R^2


Option: 3

B=\frac{2 \pi m v}{e} \text { and } K=2 m r^2 v^2 R^2


Option: 4

B=\frac{m v}{e} \text { and } K=m^2 \pi V R^2


Answers (1)

best_answer

Time period of cyclotron is

\begin{aligned} & T=\frac{1}{v}=\frac{2 \pi m}{e e B} ; B=\frac{2 \pi m}{e} v ; R=\frac{m v}{e B}=\frac{P}{e B} \\ & \Rightarrow P=e B R=e \times \frac{2 \pi m v}{e} R=2 \pi m v R \\ & K \cdot E \cdot=\frac{P^2}{2 m}=\frac{(2 \pi m v R)^2}{2 m}=2 \pi^2 m v^2 R^2 . \end{aligned}

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Riya

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