Phase difference between magnetic and electric field

[Tazerfish]

When solving the differential equations for an electromagnetic wave you get out that the electric and magnetic field oscillate in phase.
But when considering a oscillating dipole, the electric and magnetic field at a point close to the dipole are a quater period out of phase.

Can someone please explain how the initial "near field" wave becomes the "far field" wave ?
I would prefer a somewhat intuitive explanation, but a purely mathematical one isn't going to kill me .

 

[Simon Bridge]

You want the interstitial form of the EM wave?
Both solutions are approximations to the complete solution, neither are complete.

Intuitively: using gravity as an analogy ...
When you drop a mass from a short height, the "short distance" field approximation for gravity is used. For very tall heights, the "long distance" field approximation is used. Your question amounts to asking how the long distance solutions turn into the short distance solutions.

It may help to review:
http://web.mit.edu/8.02T/www/materials/Presentations/Presentation_W14D2.pdf

 

[Tazerfish]

But isn't gravity a bit of a disanalogy in this case ?
I don't know what you mean by "long distance" approximation. You could just as well use this formula $a= \frac{GM}{r^2}$.
Without considering relativistic effects you would be done at that point.
No approximations needed.It would be ideal if something like that would work for my problem as well.

You perfectly understood my question, yet the answer was a little unsatisfying.(I don't mean to be rude in saying that.)
I am still no closer to imagining or calculating the intermediate states.
And if somebody would ask me to explain (probably from maxwells equations) why the near field wave cannot persist and why it changes into the far field wave I would be completely stumped.
I feel like that is a gap in my knowledge and intuition that really could and should be filled.

 

[sophiecentaur]

You perfectly understood my question, yet the answer was a little unsatisfying.

OK. Here's an arm waving electrical explanation.
The current phase at the feed point of a transmitting dipole is (more or less) in quadrature with the voltage. You can say that, in the vicinity of the dipole the E field is due to the volts and the H field is due to the Current. But it isn't exactly in quadrature because there is a Resistive component in the Impedance at the feed point. It is that resistance (the Radiation Resistance) that accounts for the power that's actually radiated. That's due to the In Phase components of the V and I.
At a distance, the Power that's radiated must be due to in-phase E and H; the quadrature parts of the fields have died out because no power is transported away due to them. At switch-on, these reactive fields take some time to establish themselves because they actually store Energy.
What happens in the middle distance is much harder to calculate - above my pay grade - but it needs to be considered with multiple element array design where the elements interact with each other. The Mutual Impedance between elements will be resistive and reactive and is very dependent on separation, passing through all quadrants of the complex impedance. https://www.researchgate.net/publication/224692647_Receiving_Mutual_Impedance_between_Two_Parallel_Dipole_Antennas shows what I mean. It isn't an 'explanation but it does show how the relative amounts of in phase and quadrature will vary as the distance increases. It ends up 'all resistive' at great distance of course.

 

[Tazerfish]

OK. Here's an arm waving electrical explanation.
The current phase at the feed point of a transmitting dipole is (more or less) in quadrature with the voltage. You can say that, in the vicinity of the dipole the E field is due to the volts and the H field is due to the Current. But it isn't exactly in quadrature because there is a Resistive component in the Impedance at the feed point. It is that resistance (the Radiation Resistance) that accounts for the power that's actually radiated. That's due to the In Phase components of the V and I.
At a distance, the Power that's radiated must be due to in-phase E and H; the quadrature parts of the fields have died out because no power is transported away due to them. At switch-on, these reactive fields take some time to establish themselves because they actually store Energy.
What happens in the middle distance is much harder to calculate - above my pay grade - but it needs to be considered with multiple element array design where the elements interact with each other. The Mutual Impedance between elements will be resistive and reactive and is very dependent on separation, passing through all quadrants of the complex impedance. https://www.researchgate.net/publication/224692647_Receiving_Mutual_Impedance_between_Two_Parallel_Dipole_Antennas shows what I mean. It isn't an 'explanation but it does show how the relative amounts of in phase and quadrature will vary as the distance increases. It ends up 'all resistive' at great distance of course.

Thanks, that was very helpful :D
I am a big fan of arm waving electrical explanations

 

[Khashishi]

Near field is basically the electrostatic solution. You don't have "waves", just charges and the fields that surround the charges.
Far field is just the waves. If you made the charges magically disappear, you would still have waves propagating outward.

 

[sophiecentaur]

Near field is basically the electrostatic solution.

Why only 'Electrostatic"? What would you get with a loop antenna?

 

[Khashishi]

I made a mistake. Ignore my post.