Method of image charges: any extension for oscillating fields?

In summary, the conversation discusses the possibility of extending the "Method of image charges" to oscillating charges in the context of radiating problems. The speaker is interested in exploring this method in the near-field of an electrostatic antenna, but emphasizes the importance of ensuring causality. The other person suggests looking into image currents and their use in antennas, but the speaker requests for references on this topic.
  • #1
lalbatros
1,256
2
I was wondering if the "Method of image charges" could be extended even partly or approximately to oscillating charges.

I am not considering nearly-static problems, but really radiating problems.
After all, the Poisson equation and the wave equation are rather close !
Therefore, I thought that maybe in the near-field of an (electrostatic) antenna there could be a way to re-use this good old method.
I must stress however that I want causality to be (reasonnably) ensured, as I am mainly interrested in phase and group velocities results.

Have you seem somthing similar?
Thanks
 
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  • #2
Sure, take a look at image currents. Many antennas, i.e. whip and monopole, use a ground plane and image theory in their operation.
 
  • #3
Born2bwire said:
Sure, take a look at image currents. Many antennas, i.e. whip and monopole, use a ground plane and image theory in their operation.

Born2bwire,

Of course, alternative fields can produce alternating images.
However, this does not imply that this would lead to a useful image method of calculation.
For static fields, the method is obvious and simple, when applicable.
However, for alternating fields, delays have to be taken into account.
For my application (pedagogical), I need to keep a good account of these causal delays.
Would you have some reference for your suggestion?

Tanks!
 

What is the method of image charges?

The method of image charges is a mathematical technique used in electrostatics and electrodynamics to simplify the calculation of electric fields and potentials in the presence of conductive boundaries. It involves replacing a charged object inside a conductor with a system of imaginary point charges outside the conductor, known as image charges.

How is the method of image charges different for oscillating fields?

The method of image charges only applies to static electric fields. For oscillating fields, the concept of image charges can be extended by considering the time-varying potential as a superposition of static potentials. This is known as the "quasistatic approximation" and can be used to approximate the behavior of oscillating electric fields near conductive boundaries.

What are the limitations of the method of image charges for oscillating fields?

The method of image charges for oscillating fields is only an approximation and may not accurately represent the behavior of the electric field near conductive boundaries. It also does not take into account any dispersive effects, such as the frequency-dependent dielectric properties of materials.

How is the method of image charges used in practical applications?

The method of image charges is commonly used in the design of electronic components, such as antennas and integrated circuits, where conductive boundaries can significantly affect the behavior of electric fields. It is also used in theoretical studies and simulations of electromagnetic phenomena.

Are there any alternative methods to the method of image charges for oscillating fields?

Yes, there are alternative methods for calculating electric fields in the presence of conductive boundaries, such as the method of moments and the finite element method. These methods take into account more complex boundary conditions and can provide more accurate results than the method of image charges. However, they are also more computationally intensive and may not always be necessary for simple cases.

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