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If I have an antenna (let's say a short dipole antenna) it radiates an EM field in both longitudinal and transverse directions, I am aware that the longitudinal component will decrease faster (1/r^2 against 1/r) and the transverse component will be the only important one for long distances, but the longitudinal field will never disappear entirely, so this means that in all space there will exist a longitudinal field. I find this contradictory to the idea that in free space E and B fields are always transverse to the direction of propagation What am I missing?

Qmechanic
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diegobatt
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  • I don't think you're missing anything, what you say is true. – kotozna Jan 08 '17 at 19:08
  • But if i look at a far region of space where there are no sources, the Maxwell equations impose that the EM fields must be transverse to the direction of propagation. This seems contradictory to the longitudinal fields exiting in all space – diegobatt Jan 08 '17 at 19:14
  • How do you define a unique propagation direction when you have a finite size source? – Raziman T V Jan 08 '17 at 19:37
  • When finding the radiated fields in the case of the short dipole an exp(j(wt-kr)) appears, I assumed that that means that the propagation of the wave is radial, isn't that correct? – diegobatt Jan 08 '17 at 19:48
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    Related: http://physics.stackexchange.com/q/22170/2451 , http://physics.stackexchange.com/q/103171/2451 , http://physics.stackexchange.com/q/138770/2451 , http://physics.stackexchange.com/q/303724/2451 and links therein. – Qmechanic Jan 08 '17 at 19:52
  • You already showed that a solution to Maxwell's equations in a region far away from sources can contain longitudinal fields. @Raziman T.V. I think the OP is referring to standard dipole antenna solution (i.e. not actually finite size). – kotozna Jan 08 '17 at 20:04
  • But in a región of space where don't exist sources the Maxwell equations Nabla.E = Nabla.B =0 impose that the EM fields should be transverse to the direction of propagation, don't they? – diegobatt Jan 08 '17 at 20:19
  • I was thinking of vector potential but you're asking for actual fields.From memory I think only the vector potential has a radial component (but not the electric field). If you post a link to equations you're using may be able to help more. Also mention what coordinate system we are discussing (ie "radial"), spherical or cylindrical solution? – kotozna Jan 08 '17 at 20:23
  • Pag 8 to 10 of: http://es.slideshare.net/mobile/wilsonapontehuamantinco/radiacion-electromagnetica-59889633 I'm sorry it is in Spanish but it is the exact same configuration I am talking. The electric field has a radial component which is the direction of propagation of the wave. – diegobatt Jan 08 '17 at 20:34
  • It looks from the document (spherical coordinates) that although the electric field has a radial component in some places, at those places the direction of the EM wave is not radial, so the field can still be transverse. Maybe part of the confusion is you imagine dipole radiation as radial. You can check this by calculating the Poytning flux $S=E \times B$, which gives the direction of propagation and then the field must be perpendicular to this. – kotozna Jan 08 '17 at 21:53
  • Is the direction of the poynting vector always the direction of propagation? That would seem to answer my question, add it as an answer so I can punctuate it – diegobatt Jan 08 '17 at 22:18
  • No, actually it isn't. The direction of propagation I think is along r, since that's what appears in the eikonal. I am looking at eqn 9.18 of Jackson, there it seems the near field electric field can have a component along r, which means only the magnetic field is transverse. So, I think longitudinal waves must be possible. – kotozna Jan 08 '17 at 23:31
  • I think the solution is in this link's answer http://physics.stackexchange.com/questions/303724/are-all-electromagnetic-waves-transverse-in-free-space – diegobatt Jan 09 '17 at 00:39

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