This shows why there can never be residual "magnetism" left over for use in a free energy system. It states that the magnetic field B has divergence equal to zero. It is equivalent to the statement that magnetic monopoles do not exist. In other words, all magnetism comes in a dipole moment.
There is simply no way to destabilize the magnetic field without a monopole.
Do you mean quaternions?
I'm not sure if you are referring to James Clerk Maxwell's original quaternion (a field equation), or a Heavyside altered one (a vector equation).
You may know this but for everyone else:
Only four quaternions from Maxwell's original 200 are accepted - the other 196 were dismissed as abominations. And those four were changed from field to vector. Taken together, they describe the entirety of electromagnetic radiation.
As for the other 196 - they languish in obscurity since the self-educated Heavyside dismissed them in the 19 Century.
my 2.5 cents - was 2 cents but I had to raise my rates in January.