Helmholz equation If we combine the two curl equations we find
curl curl E = ω2²μE. The vector identity curl curl = grad div−∇2 gives, in view of the fact that div E = 0,
∇2E = −ω2²μE . (8.6)
This equation is known as the three-dimensional wave equation and we will be concerned
with various of its solutions. When any solution for E is known we can calculate
the accompanying H from equation 8.1 above.
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