Maxwell's equations Poynting's theorem time-harmonic fields

Maxwell’s equations

Poynting’s theorem 1852-1914

electromagnetic fields Time harmonic electromagnetic fields

Assume that the excitation signal is a time harmonic signal. All electromagnetic fields will also have a time harmonic variation. Therefore:

Maxwell's equations

Maxwell's equations

Poynting's theorem This was “0” back in my day also. time average

Poynting's theorem

Poynting's theorem

Poynting's theorem not equal to 0 equal to 0 real power

right hand rule Poynting's theorem power lost power stored energy

radiated electromagnetic power density, These are: radiated electromagnetic power density, dissipated electromagnetic power density, and stored electromagnetic energy density. You must integrate the equations over a volume of interest.

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Find the displacement current. area A Vd

Phasor < = = > time domain

Phasor < = = > time domain

At what frequency will a lossy dielectric act like a conductor? conduction current displacement current

Show that the conduction current and the displacement current differ in phase.

boundary conditions for time varying fields tangential electric fields are continuous normal components of displacement flux density differ by a surface charge density

boundary conditions for time varying fields tangential magnetic field intensities differ by a surface current density normal components of magnetic flux density are continuous

Use the “right hand rule” with Poynting’s Theorem!