Formula: Circular Motion in a Magnetic Field Cyclotron radius Velocity Electric charge Mass Magnetic flux density (B-field)
$$r ~=~ \frac{ \class{brown}{m} \, \class{blue}{v} }{ |q| \, \class{violet}{B} }$$
$$r ~=~ \frac{ \class{brown}{m} \, \class{blue}{v} }{ |q| \, \class{violet}{B} }$$
$$\class{blue}{v} ~=~ \frac{ |q| \, \class{violet}{B} \, r }{ \class{brown}{m} }$$
$$|q| ~=~ \frac{ \class{brown}{m} \, \class{blue}{v} }{ r \, \class{violet}{B} }$$
$$\class{brown}{m} ~=~ \frac{ |q| \, \class{violet}{B} \, r }{ \class{blue}{v} }$$
$$\class{violet}{B} ~=~ \frac{ \class{brown}{m} \, \class{blue}{v} }{ r \, |q| }$$
Cyclotron radius
$$ r $$ Unit $$ \mathrm{m} $$
Cyclotron radius (also called Larmor radius) is the radius of the circular path along which a moving charge moves due to the Lorentz force.
Velocity
$$ \class{blue}{\boldsymbol v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Velocity component of the orbiting charge perpendicular to the magnetic field.
Charge
$$ |q| $$ Unit $$ \mathrm{C} = \mathrm{As} $$
Amount of electric charge of the orbiting particle.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the orbiting charged particle.
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$
Magnetic field through which the charge moves.