Question

Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is ______.

Options

• `("q"^2"B")/(2pi"m")`

• `("q""B")/(2pi"m")`

• `("q""B"^2)/(2pi"m")`

• `("q""B")/(pi"m")`

Answer 1

Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is `underline(("q""B")/(2pi"m"))`.

Explanation:

When a charge q particle moves at speed v through a magnetic field B, it encounters the magnetic Lorentz force, which acts as a centripetal force.

Therefore, we have

`"mv"^2/"r" = "Bqv"`

`"v"/"r" = "Bq"//"m"`

`omega` = Bq/m

v = Bq/2πm    `(omega = 2pi"v")`

here, v is the cyclotron frequency.