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A well-known application of the duality you refer to occurs in the design of antennas, for example, magnetic vs. electric dipole antennas. A magnetic dipole is a loop antenna, an electric dipole is a linear antenna, still their radiation pattern is similar as one replaces E with H.


The idea is that Maxwell's equations are symmetric under the exchange of certain quantities. This does not mean that you identify the electric and the magnetic field, but just say that they are dual to each other. This resolves your problem of dimensionality. If one extends this principle to the two equations which contain divergences of the fields, one ...

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