Wave Equation

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Maxwell's equations in differential form in a vacuum (i.e. no charges or currents present) are 

Take the curl of Eq. (1b) to obtain

Substitute Eq. (1d) in for Ñ´B to get

Using the vector identity Ñ´ (Ñ´E) = Ñ(Ñ·E) - ѲE = - ѲE and Eq. (1a) we get

This result has the form of a (vector) wave equation.  The wave travels at c = 2.9979´108 m/s. Take the curl of Eq. (1d) we get

Substitute Ñ´ (Ñ´B) = Ñ(Ñ·B) - ѲB  = - ѲB and Eq. (1c) to yield

This result is also a wave equation for the vector field B.

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