  The method of retarded potentials is used to derive the Biot-Savart law,
taking into account the correction that describes the chaotic motion of charged
particles in rectilinear currents. Then this method is used for circular
currents and the following theorem is proved: The magnetic field on the
rotation axis of an axisymmetric charged body or charge distribution has only
one component directed along the rotation axis, and the magnetic field is
expressed through the surface integral, which does not require integration over
the azimuthal angle . In the general case, for arbitrary charge distribution
and for any location of the rotation axis, the magnetic field is expressed
through the volume integral, in which the integrand does not depend on the
angle . The obtained simple formulas in cylindrical and spherical coordinates
allow us to quickly find the external and central magnetic field of rotating
bodies on the rotation axis.
