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The directional energy flux of an electromagnetic field. In conjunction with Poynting's theorem and the continuity equation, it used to express the conservation of electromagnetic energy, and to calculate the power flow in electric and magnetic fields.
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Is the Poynting vector continuous?
Helmholtz equation for the magnetic field is
$$∇^2 \mathbf{H} + k^2 \mathbf{H} = \mathbf{0}$$
Assuming time-harmonic waves Ampere's law can be rearranged
$$\mathbf{E} = \frac{∇\times\mathbf{H}}{σ+j …