Galilean electromagnetism is useful for describing the electric and magnetic fields in the vicinity of charged bodies moving at non-relativistic speeds relative to the frame of reference.
[a]: 12 In electrical networks, Galilean electromagnetism provides possible tools to derive the equations used in low-frequency approximations in order to quantify the current crossing a capacitor or the voltage induced in a coil.
According to Germain Rousseaux,[1] the existence of these two exclusive limits explains why electromagnetism has long been thought to be incompatible with Galilean transformations.
Einstein has then allowed a generalization of Newton's laws of motion to describe the trajectories of bodies moving at relativistic speeds.
In the electromagnetic frame, James Clerk Maxwell directly derived the equations in their relativistic form, although this property had to wait for Hendrik Lorentz and Einstein to be discovered.
In 1973 Michel Le Bellac and Jean-Marc Lévy-Leblond[6] state that these equations are incorrect or misleading because they do not correspond to any consistent Galilean limit.