# Time Harmonic Form of Maxwell's Equations.

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Assume that both the E field an the B field are time-harmonic, so that each can be written as:

E = E(0)exp(i(k*r-wt))

B = B(0)exp(i(k*r-wt)) where * = dot

The time and spatial derivatives can then be written as

partial of E with respect to t = -iwE

Partial of B with respect to t = -iwB

divergence of E = ik*E

curl of E = ik x E

curl of B = ik x B

The divergence of B, as always, is zero. Now rewrite Maxwell's equations componentwise, using the derivatives of the time-harmonic form.

(Please see the attachment for the complete formula.)

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