maxwell's equations and hodge theory

How is Hodge theory of harmonic forms related to maxwell's equations.Atiyah says that Hodge was directly motivated by considerations of maxwell's equations while commenting on donaldson.

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Actually it's the fieldstrength which is harmonic. Maxwell's equations in vacuo are dF =0 \qquad\text{and}\qquad d\star F = 0$, where$F\$ is the fieldstrength 2-form. –  José Figueroa-O'Farrill Mar 11 '13 at 8:52