When a vector field representing a physical quantity (e.g. B) has ∇[itex]\cdot[/itex]B = 0 what is then the physical interpretation of this? Some people have said that the field doesn't diverge away from anything, but as far as I can tell magnetic field can easily get weaker and weaker the further you go away. I also have some trouble understanding exactly what my book means by the fact that ∇[itex]\cdot[/itex]B = 0 reflects the fact that there exists no magnetic charge. I know in the electrical case ∇[itex]\cdot[/itex]E = ρ/ε0 but that just comes from coulombs law and how electric fields behave. Who says magnetic charge can't be different producing fields with zero divergence (like that of the Biot-Savart law).