  In the present article, we discuss a modification of classical
electrodynamics in which ``ordinary'' point charges are absent. The modified
equations contain additional terms describing the induced charges and currents.
The densities of the induced charges and currents depend on the vector k and
the vectors of the electromagnetic field E and B. It is shown that the vectors
E and B can be defined in terms of two 4-potentials and the components of k are
the components of the 4-tensor of the third rank. The Lagrangian of modified
electrodynamics is defined. The conditions are derived at which only one
4-potential determines the behavior of the electromagnetic field. It is also
shown that static modified electrodynamics can describe the electromagnetic
field in the inner region of the electric monopole. In the outer region of the
electric monopole the electric field is governed by the Maxwell equations. It
follows from boundary conditions at the interface between the inner and outer
regions of the monopole that the vector k has a discrete spectrum. The electric
and magnetic fields, energy and angular momentum of the monopole are found for
different eigenvalues of k.
