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Olympiad workbook

Exam: Olympiad workbook
Subject: NSEP
Chapter: Electrostatics

Olympiad workbook · NSEP · Electrostatics

The frequency of the transverse oscillations of a proton (mass M)...

The frequency of the transverse oscillations of a proton (mass M) trapped in a cylindrical relativistic electron beam of circular cross section of radius R and current

I

is given by [assume that speed v of relativistic electrons

\approx c

(the speed of light in vacuum) and ignore magnetic effect]

Options

A $\frac{1}{2 \pi R} \sqrt{\frac{e I}{2 \pi \varepsilon_0 M c}}$
B $\frac{1}{2 \pi \mathrm{R}} \sqrt{\frac{2 \pi \varepsilon_0 I}{M c}}$
C $\frac{1}{\mathrm{R}} \sqrt{\frac{2 \pi \varepsilon_0 M c}{\mathrm{e} I}}$
D $\frac{1}{2 \pi \varepsilon_0} \sqrt{\frac{2 \pi \varepsilon_0 M c}{\mathrm{e} I}}$

Correct answer

A. $\frac{1}{2 \pi R} \sqrt{\frac{e I}{2 \pi \varepsilon_0 M c}}$

Step-by-step solution

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