Formula: Charge in the Magnetic Field (Cyclotron Frequency)
$$f ~=~ \frac{|q| \, \class{violet}{B}}{2\pi \, \class{brown}{m}}$$
$$f ~=~ \frac{|q| \, \class{violet}{B}}{2\pi \, \class{brown}{m}}$$
$$\class{violet}{B} ~=~ \frac{2\pi \, \class{brown}{m} \, f}{|q|}$$
$$|q| ~=~ \frac{2\pi \, \class{brown}{m} \, f}{\class{violet}{B}}$$
$$\class{brown}{m} ~=~ \frac{|q| \, \class{violet}{B}}{2\pi \, f}$$
Cyclotron Frequency
$$ f $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$
Cyclotron frequency is the frequency at which a charged particle travels a circular path in the magnetic field. It therefore describes how many circular revolutions the particle performs per second.
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$
The external magnetic field in which the particle moves. The motion of the particle is perpendicular to the magnetic field.
Electric charge
$$ |q| $$ Unit $$ \mathrm{C} = \mathrm{As} $$
Electric charge performing a circular orbit in the magnetic field. Here, the magnitude of the charge is considered to avoid a negative cyclotron frequency.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the charged particle.
Pi
$$ \pi $$ Unit $$ - $$
Pi is a mathematical constant and has the value: \( \pi ~=~ 3.1415926... \)