According to Coulomb law, why do fixed charges interact, if they don't emit the photons? Why does it happens, if fixed charges don't oscillate the em field?

 A: Coulombs law developed from the observation of the interaction of charges, and started as classical physics. Photons are in the realm of quantum mechanics, as they are elementary particles.
Elementary particles obey Coulombs law , but the equations used are quantum mechanical equations, where the coulomb potential is used, between two electrons, for example. In quantum field theory, a calculational tool at the quantum level, the two electrons exchange virtual photons, and that is how the interaction is explained, quantum mechanically.

One should not confuse the classical electricity and magnetism framework of macroscopic interactions with the microcosm where quantum mechanics reigns. Photons belong to quantum mechanics. charges exist in both frames, but different mathematical models describe the data.
A: As i understoot, since the fixed charge are not emitting photon but they have their electric and magnetic fields .the energy is emitted from the charge particle only when particle in motion .since particle is not moving it will have fixed electric and magnetic field and thus there is no disturbance in these field lines ,now since energy is carried by the waves caused by the disturbance in electric and magnetic fields .hence there is no energy traveled .there fore a charge particle can interact with other charge particle  without emitting photon(energy)only through the ineraction between their electric and magnetic fields
