The Absence of Magnetic Charge

The important result ∇. B = 0 is one of Maxwell’s equations. We can get an interpretation of the equation. ∇. B = 0, by comparing it with the analogous equation for the electric field, namely ∇. E = ρ/ϵ0. Here, ρ is the net charge density and arises because electric charge exists in individual units of opposite sign so that it is possible to have ρ≠0 by having an excess of one sign or another. But we see from the equation ∇. B = 0 that such a situation cannot arise in the magnetic case and therefore there cannot be individual units of charge analogous to electric charge. Such magnetic charges are called magnetic monopoles. Although their existence has been shown to be compatible with the requirements of quantum mechanics, every experimental search that has been made for them has been unsuccessful. Consequently, until any such time that magnetic monopoles have been unambiguously found to actually exist, we must continue to write ∇.B = 0 and remember that the sources of B are only always currents.


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