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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