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]

A

$$\frac{1}{2\pi R}\sqrt{\frac{eI}{2\pi\varepsilon_0 Mc}}$$

B

$$\frac{1}{2\pi R}\sqrt{\frac{2\pi\varepsilon_0 I}{Mc}}$$

C

$$\frac{1}{ R}\sqrt{\frac{2\pi\varepsilon_0 Mc}{eI}}$$

D

$$\frac{1}{2\pi \varepsilon_0}\sqrt{\frac{2\pi\varepsilon_0 Mc}{eI}}$$