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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 to accelerate protons (mass = m). The operating magnetic field (B) used in t

An alternating electric field, of frequency v, 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 :

Option: 1

\mathrm{\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}} ~and ~K=2 m \pi^2 v^2 R^2}


Option: 2

\mathrm{\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}} ~and ~K=m^2 \pi v R^2}


Option: 3

\mathrm{\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}} ~and ~K=2 m \pi^2 v^2 R}


Option: 4

\mathrm{\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}} ~and ~K=m^2 \pi v R^2}


Answers (1)

best_answer

Time period of cyclotron is.
\mathrm{T}=\frac{1}{\mathrm{v}}=\frac{2 \pi \mathrm{m}}{\mathrm{eB}} ; \mathrm{B}=\frac{2 \pi \mathrm{m}}{\mathrm{e}} \mathrm{v} ;=\frac{\mathrm{mv}}{\mathrm{eB}}=\frac{\mathrm{p}}{\mathrm{eB}} \\
\mathrm{ \Rightarrow P=e B R=\mathrm{e} \times \frac{2 \pi \mathrm{mv}}{\mathrm{e}} R=2 \pi m v R }
\mathrm{ \text { K.E. }=\frac{\mathrm{p}^2}{2 \mathrm{~m}}=\frac{(2 \pi \mathrm{muR})^2}{2 \mathrm{~m}}=2 \pi^2 m v^2 R^2}

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Gunjita

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