This may be a duplicate, but how are (ideally) constant E- and B-/H-fields transmitted thru space? In this situation I like think of EM radiation as a note from a particle informing the universe of a change, but as the fields are constant, there aren't any notes/photons to send. For example, how will a bar magnet affect a cosmic ray passing by earth, and by what mechanism? Is this the province of virtual photons, or something else?
One has to define in what framework one is talking of electric and magnetic fields.
In the classical framework the field is defined, for simplicity lets take a point charge, as proportional to 1/r^2 and exists up to infinity. Thus classically there is no transmission for a static charge, it just is. When a charge is moving, i.e. changing its (x,y,z,t) dependence radiation is emitted, if there exists acceleration, as electromagnetic waves. The effect of the classical motion of these charges and consequent motion of field lines can be seen in this simulation . A video of constant motion ( non radiating) is here . It is a subject of interest for plasma physics. Another way of looking at static fields is that they are built up of electromagnetic fields of wavelength approaching infinity.
This brings us to the quantum framework, which as far as we have discovered with our experiments, is the fundamental underlying level of physics from which all classical theories emerge.
For example, how will a bar magnet affect a cosmic ray passing by earth, and by what mechanism? Is this the province of virtual photons, or something else?
Photons exist in the quantum mechanical domain and the classical electromagnetic field emerges from a large ensemble of photons. In this framework all information is transmitted by particles . So virtual photons will be transmitted between the bar of magnet and the cosmic ray with the velocity of light , though the effect will be infinitesimal. Virtual means that the exchange happens between known input and output particles and the exchanged photon is not on mass shell. Your example can be written up as such an interaction and the probability of the bar of magnet to change to path of the cosmic ray can be computed but it is not worth the trouble because it will be very very small ( 1/r^2 may be disguised in the solutions of the quantum mechanical problem but it is still there).