Electric surface current on a PEC

• EmilyRuck
In summary: Impressions do not carry the charges in the PEC, they carry external agents which induce a current in the PEC. This current acts to effectively short out the current (reciprocity is a nice way to prove this). So the boundary conditions on the magnetic field are not affected.
EmilyRuck
Hello!
When considering the boundary conditions for the electromagnetic field $\mathbf{E}, \mathbf{H}$ on the surface of a Perfect Eletric Conductor we have:
• $\mathbf{E} \times \mathbf{\hat{n}} = 0$
• $\mathbf{J}_S = \mathbf{\hat{n}} \times \mathbf{H}$
the tangential electric field should vahish, while the tangential magnetic field is discontinuous and the discontinuity generates the surface current density.

The current density flows on the surface a PEC, so we can consider as an equivalent situation the superposition of $\mathbf{J}_S$ and its image current, which is exactly opposite of $\mathbf{J}_S$: the net current is 0 (this argument is used in order to prove that an electric current flowing on a PEC does not radiate).

But doesn't this affect the boundary conditions on the magnetic field? If the current is zero, why the relative boundary condition is not written as $0 = \mathbf{\hat{n}} \times \mathbf{H}$?!

Emily

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

EmilyRuck said:
The current density flows on the surface a PEC, so we can consider as an equivalent situation the superposition of $\mathbf{J}_S$ and its image current, which is exactly opposite of $\mathbf{J}_S$: the net current is 0 (this argument is used in order to prove that an electric current flowing on a PEC does not radiate).

Emily

Not quite. I think you are confusing impressed currents and induced currents. impressed currents are not carried by the charges in the PEC; they are carried by external agents. When you impress an electric arbitrarily close to a PEC (like you might do when invoking equivalence theorems), it induces a current in the PEC that acts to effectively short out the current (reciprocity is a nice way to prove this).

For the rest of your question, consider the simple case of a plane wave normally incident on a plane PEC. The total H field on the surface is twice the incident field, which should allow you to compute the electric surface current on the PEC. This surface current on the PEC is radiating the reflected electromagnetic wave.

jason

EM_Guy and EmilyRuck
EmilyRuck said:
The current density flows on the surface a PEC, so we can consider as an equivalent situation the superposition of JS\mathbf{J}_S and its image current, which is exactly opposite of JS\mathbf{J}_S: the net current is 0 (this argument is used in order to prove that an electric current flowing on a PEC does not radiate).
What does this mean? There is no "image current".

Thank you for your answers and sorry for the great delay. It was misleading to me the fact that for several days there were no replies.
Thank you jasonRF for your complete and useful answers. For Meir Achuz: as said by jasonRF, I made a little confusion between impressed currents and induced currents.

1. What is an electric surface current on a PEC?

An electric surface current on a PEC (perfectly electrically conducting) material refers to the flow of electric charge along the surface of the material. This is often observed in conductors such as metals, where the free electrons can easily move along the surface.

2. How is an electric surface current different from an electric current?

An electric surface current is a type of electric current that flows only on the surface of a material, while an electric current can flow through the entire volume of a material. Electric surface currents are often induced by external electric fields or currents flowing through nearby conductors.

3. What factors affect the magnitude of an electric surface current?

The magnitude of an electric surface current on a PEC is affected by several factors, including the strength of the external electric field, the conductivity of the material, and the geometry of the material. In general, materials with higher conductivity and larger surface areas will exhibit stronger electric surface currents.

4. How can electric surface currents be measured?

Electric surface currents can be measured using various techniques, such as surface current probes or Hall effect sensors. These devices can detect the magnetic field produced by the surface current and convert it into an electric signal that can be measured.

5. What are the applications of electric surface currents on PEC materials?

Electric surface currents on PEC materials have various applications, including in antennas, electromagnetic shielding, and current-carrying structures. They are also important in understanding the behavior of electromagnetic waves and their interactions with conductors.

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