Question

A cyclotron's oscillator frequency is 'n' and radius of the dees is 'r'. The operating magnetic field (B) for accelerating protons of charge 'q' and kinetic energy of protons produced by the accelerator is respectively ('m' and 'v' be the mass and velocity of proton).

Options

• `(pi"nm")/"q", "qvBr"/2`

• `(2pi"nm")/"q", "qvBr"`

• `(4pi"nm")/"q", "qvBr"/2`

• `(2pi"nm")/"q", "qvBr"/2`

Answer 1

`(2pi"nm")/"q", "qvBr"/2`

Explanation:

clotron frequency n = `"qB"/(2pi"m")`

`therefore "B" = (2pi"nm")/"q"`

Also, `"mv"^2/"r" = "q ∨ B"`

`therefore "mv"^2` = q ∨ B r

K.E. = `1/2 "mv"^2 = "qvBr"/2`