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The radius of the circle along which an electrically charged particle moves in a plane perpendicular to a magnetic field with magnetic induction  $  \mathbf B $. 
The motion of the charge  $  e $
in a uniform magnetic field takes place under the action of the Lorentz force and is described by the equation

\begin{equation}
 \label{eq1}
\frac{\partial  \mathbf p }{\partial  t }
  = e [ \mathbf v , \mathbf B ] ,
\end{equation}

where  $  \mathbf p $
is the momentum of the charged particle and  $  \mathbf v $
is the velocity of the charge in the laboratory reference frame. The solution of \eqref{eq1} in a Cartesian coordinate system with the  $  z $-
axis directed along the field  $  \mathbf B $
has the form

$$ \tag{2 }
v _ {x}  =  v _ {0t}  \cos ( \omega _ {L} t + \alpha ) ,\ \ 
v _ {y}  =  - v _ {0t}  \sin ( \omega _ {L} t + \alpha ) ,\ \ 
$$

$$ 
v _ {z}  =  v _ {0z} ,
$$

$$ 
x  =  x _ {0} + r  \sin ( \omega _ {L} t + \alpha ) ,\  y
 =  y _ {0} + r  \cos ( \omega _ {L} t + \alpha ) ,
$$

$$ 
z  =  z _ {0} + v _ {0z} t ,
$$

where  $  \omega _ {L} = e c  ^ {2} \mathbf B / \epsilon $
is the so-called Larmor frequency,  $  \epsilon $
is the energy of the charged particle, which does not change under motion in a uniform magnetic field,  $  v _ {0t} $, 
$  v _ {0z} $, 
$  \alpha $, 
$  x _ {0} $, 
$  y _ {0} $, 
$  z _ {0} $
are constants determined from the initial conditions, and

$$ 
r  =  
\frac{v _ {0t} }{\omega _ {L} }
  = \ 

\frac{v _ {0t} \epsilon }{e c  ^ {2} | \mathbf B | }

$$

is the Larmor radius. In a uniform magnetic field the charge moves along a helix with axis along the magnetic field and Larmor radius  $  r $. 
The velocity of the particle is constant.

If the velocity of the particle is small compared with the velocity of light, one can put approximately  $  \epsilon = mc  ^ {2} $
and the expression for the Larmor radius takes the form

$$ 
r  =  
\frac{v _ {0t} }{\omega _ {0} }
  = \ 

\frac{v _ {0t} mc  ^ {2} }{e | \mathbf B | }
 .
$$

The magnetic moment of the system manifests itself as a result of the rotation of the charged particles in the magnetic field.

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  I.E. Tamm,   "Fundamentals of the theory of electricity" , MIR  (1979)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  L.D. Landau,   E.M. Lifshitz,   "The classical theory of fields" , Addison-Wesley  (1951)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  P.C. Clemmow,   J.P. Dougherty,   "Electrodynamics of particles and plasmas" , Addison-Wesley  (1969)</TD></TR>
</table>