Posts Tagged ‘multivariable calculus’

More Magnetic Monopoles, With a Summery Hint of Maxwell’s Equations

June 9, 2008

It was pointed out to me that perhaps last time I went off too far into the theoretical setup and didn’t quite wrap up succinctly for you what exactly a magnetic monopole is. In short, a magnetic monopole would be a particle that carries magnetic charge, like how electrons and protons are carriers of electric charge. A bar magnet has two poles, and if you cut it in half, it still has two poles. If you keep cutting it in half and break it down as far as it will go, you will have a spinning electron which still has a “North” and a “South” pole. Whereas, in seeking the most simple possible configuration that produces an electric field, if you broke down a material as far as it would go you would have a single electron radiating a uniform electric field in all directions. This electric field wouldn’t pull objects toward it on one side and push objects away on the other like a dipole; it’s uniform in all directions (pictured here is the electric field of a positive point charge. An electron is a negative charge, so the direction of the field in reversed — pointing in toward the electron — but you get the idea). An electron is an example of an electric monopole. Similarly, a magnetic monopole, which is a magnetic charge, would have a uniform magnetic field radiating uniformly in all directions.

It’s not for the faint of heart, but for those willing to brave some math, I’ve got more for you on Maxwell’s equations, and how they would be symmetrical if a magnetic charge existed. Look at the pretty equations and skip to the summary just above the second set of equations if your eyes start glazing over. These are Maxwell’s equations for charges and electric and magnetic fields in a vacuum:

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