  The electromagnetic field in a magnetized neutron star and the underlying
volume charges and currents are found. A general case of a rigidly rotating
neutron star with infinite conductivity, arbitrary distribution of the internal
magnetic field, arbitrarily changing angular velocity, and arbitrary surface
velocity less than the velocity of light is considered. Quaternions are used to
describe rotation and determine the magnetic field. It is shown that the charge
density is not equal to and can exceed significantly the common
Goldreich-Julian density. Moreover, corrections to the magnetic field due to
stellar rotation are zero. For a rotating neutron star, twisting magnetic field
lines causes charge accumulation and current flows. This fact shows a possible
link between changing internal magnetic field topology and observed activity of
neutron stars.
