Alright, I think I am correct on this. What I need is assurance that the magnetic monopoles are always attractive force so that unlikes attract and yet also likes attract, wherein electric charge we have both attraction and repulsion.
So my problem is to find out if the Maxwell Equations with magnetic monopoles required some negative sign somewhere to denote this special feature of magnetic monopoles.
Now it is commonsense or instinctively clear that monopoles have to be always attraction and never repulsion because in a bar magnet, one end is the north and the other is the south and if you had both repulsion with attraction, then you could never have all the "norths conglomerated" and all the "souths conglomerated" at the other end. But if magnetic monopoles were always attractive, then the norths can conglomerate and the souths can conglomerate.
So, the problem for me is to find out where I need a extra negative sign so that the Maxwell Equations with magnetic monopoles has only attraction force for magnetic monopoles.
div*E = r_E
div*B = r_B
- curlxE = dB + J_B
curlxB = dE + J_E
Now there are three likely candidates of where to add an extra negative sign. The first is Gauss's law of magnetism for it introduces the magnetic monopoles. So do we have a -div*B = r_B as the solution?
Or another spot is the Faraday law of its new term the magnetic current density as -J_B ? However, I wonder if the magnetic current density term alone, stands up and tells us that there is no repulsion force with magnetic monopoles since it is not negative termed.
Or a third spot is the Ampere/Maxwell law as -curlxB? Now if it is this term that needs a negative sign, then the Maxwell equations would be symmetrical overall and no longer asymmetrical due to the negative sign in Faraday's law. Now does it make sense? Well I think so, since the negative sign in Faraday's law yields the Lenz law that says the direction of the magnetic field is opposite to the bar magnet. So that Lenz's law with the negative sign creates a repulsion.
So is it one of these three?
I suspect it is, for I cannot see how the status quo can deliver a attraction-force-only for magnetic monopoles unless it is embedded in the positive term of magnetic current density. The more I think about this, the more I am leaning towards the positive term J_B the magnetic current density, for a density term of monopoles suggests conglomeration of monopoles of north conglomerating with north and not repelling.
So maybe I need not add a new negative sign at all and that the J_B term takes care of the idea that magnetic monopoles always attract, never repel, and that the Maxwell Equations are meant to have its slight asymmetry.
Perhaps the negative sign in Faraday's law (Lenz's law) is meant for magnetic dipoles, not monopoles and that we need to be careful in the Maxwell Equations of when we are talking of dipoles or monopoles.
Now I am probably more confused than when I had started. So I will sleep on it.
-- Approximately 90 percent of AP's posts are missing in the Google newsgroups author search starting May 2012. They call it indexing; I call it censor discrimination. Whatever the case, what is needed now is for science newsgroups like sci.physics, sci.chem, sci.bio, sci.geo.geology, sci.med, sci.paleontology, sci.astro, sci.physics.electromag to?be hosted by a University the same as what Drexel?University hosts sci.math as the Math Forum. Science needs to be in education?not in the hands of corporations chasing after the next dollar bill. Only Drexel's Math Forum has done a excellent, simple and fair author-archiving of AP sci.math posts since May 2012 as seen here :