(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples




IEVref:705-02-10ID:
Language:enStatus: Standard
Term: complex Poynting vector
Synonym1:
Synonym2:
Synonym3:
Symbol:
Definition: for a sinusoidal wave of angular frequency ω, the vector product:

1 2 E _ H _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWcaaqaaiaaigdaaeaacaaIYaaaamaaFiaabaWaaWaaaeaacaWGfbaaaaGaay51GaGaey41aq7aa8HaaeaadaadaaqaaiaadIeaaaaacaGLxdcadaahaaWcbeqaaiabgEHiQaaaaaa@4367@

when the electric field vector E (t) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaaiaadweaaiaawEniaiaacIcacaWG0bGaaiykaaaa@3E5E@ and the magnetic field vector H (t) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaaiaadweaaiaawEniaiaacIcacaWG0bGaaiykaaaa@3E5E@ are represented at the same point, in complex notation, by the equations:

E (t)=Re( E _ e jωt ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meqabaGacmGadiWaaiqabaabaiaafaaakeaadaWhcaqaaiaadweaaiaawEniaiaacIcacaWG0bGaaiykaiabg2da9iGackfacaGGLbGaaGPaVlaacIcadaadaaqaamaaFiaabaGaamyraaGaay51GaaaaiaaykW7ciGGLbWaaWbaaSqabeaacaGGQbGaeqyYdCNaamiDaaaakiaacMcaaaa@4CF4@

H (t)=Re( H _ e jωt ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meqabaGacmGadiWaaiqabaabaiaafaaakeaadaWhcaqaaiaadweaaiaawEniaiaacIcacaWG0bGaaiykaiabg2da9iGackfacaGGLbGaaGPaVlaacIcadaadaaqaamaaFiaabaGaamyraaGaay51GaaaaiaaykW7ciGGLbWaaWbaaSqabeaacaGGQbGaeqyYdCNaamiDaaaakiaacMcaaaa@4CF4@

where E _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaamyraaaaaiaawEniaaaa@3C1C@ and H _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaamyraaaaaiaawEniaaaa@3C1C@ are not time-dependent and are generally complex, H _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaamisaaaaaiaawEniamaaCaaaleqabaGaey4fIOcaaaaa@3D3B@ being the complex conjugate of H _ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbba9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meWabaGacmGadiWaaiWabaabaiaafaaakeaadaWhcaqaamaamaaabaGaamyraaaaaiaawEniaaaa@3C1C@

NOTE 1 – The real part of the complex Poynting vector is the average of the Poynting vector during one cycle.

NOTE 2 – The imaginary part of the complex Poynting vector is a vector of which, with certain reservations, the direction may be considered as being that of reactive energy propagation, and the magnitude may be regarded as the reactive power flux per unit surface area perpendicular to this direction, with a sign assigned conventionally.


Publication date:1995-09
Source:
Replaces:
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: