0 $\begingroup$ A capacitor ... To calculate the Poynting vector $\boldsymbol{P}$ we need the $\boldsymbol{E}$ and $\boldsymbol{B}$ fields. I think you neglected the capacitor displacement current. It is not informative to simply report that some source finds paradoxical results without saying what those results are and how they arrise.
On the other hand, the derivation of S, the momentum propagation parameter, involves S itself and not the divergence of S, so S does retain its meaning as the flow of momentum even for static fields. I assume that this is what is intended since in this discussion the amplitude of E does not vary with time. It is my understanding that H is corrected for magnetisation of matter, whereas B is the pure field.
I run across a lot of confusion with my students about the meaning of the Poynting vector of static fields, so I believe this section should be expanded. Learn more about Stack Overflow the company ... An 80 pF chip capacitor is inserted into the coil to achieve resonance. (3.24) The significance of the indentification of field energy density and energy flux density is For static fields, the Poynting vector only represents field momentum propagation. %PDF-1.5 A great reference for all this is in the American Journal of Physics: A nice addition to this subject could be the relation between the quantifiable energy of a photon (E=wh) to the Poynting vector and how one can be derived from and represented by the other.
xڭZ[��~�_��јo�T (�v�M�4if� H�B�5�PY�H�N����s!u�ҳ�i1���x9����D��tBIk6��6^5��/_}{��ig�7^u��i�e����������xy��r�䅤Ȥ���/��!����M*����fs��/>�R��R��1E��?��U��n��_�t)Ǻk���˭VI��~i��X�G���ma�j?v�H2컓�PE�kߍ}5�E۪?���{��8�?6�Hߝ�c[���;?��~�st��=�ȏ��)�7��,f��� i(t) = \frac{v(0)}{R} e^{-t/\tau} = \frac{Q}{\tau} e^{-t/\tau} $$Note $v=iR$ at all times (equivalent to neglecting wire inductance).To calculate the Poynting vector $\boldsymbol{P}$ we need the $\boldsymbol{E}$ and $\boldsymbol{B}$ fields.1) Neglecting fringing fields, the electric field $E$ between the capacitor plates is just $v(t)/d$ (independent of where you measure between the plates):$$ \boldsymbol{E} = - \frac{v(t)}{d} \boldsymbol{\hat{z}} I added a few years ago (2013)in this section (adding a curl of a field), the possibility to define a "magnetic free" Poynting vector that is very helpful in situation where magnetic field is negligible (and is really used). The Poynting vector correctly describes the flow of energy into the dielectric from outside the capacitor as the field in the dielectric grows, with the bulk of the energy flow being around the exterior of the capacitor depending on the exterior electric field. In Poynting's original paper and in many textbooks, the Poynting vector is defined as = ×, where bold letters represent vectors and . = -i + \pi r^2 \epsilon \frac{Q}{\tau Cd} e^{-t/\tau} For dynamic fields, the Poynting vector represents both energy flux and field momentum propagation.
Then a wire of resistance R is placed between them, how do I go about deriving a time-dependent expressiionYou have to first derive the time-dependent current $I(t)$ which runs through the wire.
If we write w 1 [B2/µ0 + 0E 2] the energ ydensit , then Poynting’s theorem is: 2 ∂w E.j = − .s − ∂t . Hello ! \boldsymbol{\hat{\theta}} $$ $$ \boldsymbol{P} = \frac{1}{\mu} \boldsymbol{E \times B} /Length 3228 By clicking “Post Your Answer”, you agree to our To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Detailed answers to any questions you might have Alfredo Narváez 2 views. Anticyclical 'vortexes' around the plates. The statement that adding the curl of a vector field to t the relationship of the noether energy-momentum tensor The charges of the discharge current are electrons. In Poynting's original paper and in many textbooks, the Poynting vector is defined asIn the "microscopic" version of Maxwell's equations, this definition must be replaced by a The Poynting vector represents the particular case of an energy flux vector for electromagnetic energy. What do you think?