# Electromagnetic plane waves from a current sheet

• Luqman Saleem
In summary, the conversation discusses an infinite sheet of time-harmonic current in the ##yz##-plane at ##x=-d## and a perfect electric conductor (PEC) half space at ##(0<x<\infty,-\infty<x,y<\infty)##. The current density on the sheet is represented by $$\mathbf{J}=\hat{z}J_0\delta(x+d)$$ and the questions revolve around finding the fields in the region and solving the problem with the presence of the PEC. The question also mentions the use of the method of images to solve the problem.
Luqman Saleem
I have an infinite sheet (in lossless, homogeneous medium) of time-harmonic current in ##yz##-plane at ##x=−d##. The current density on this sheet is given by
$$\mathbf{J}=\hat{z}J_0\delta(x+d)$$
##δ(x+d)## is delta function. Moreover, there is a perfect electric conductor (PEC) half space at ##(0<x<∞,−∞<x,y<∞)## as shown below

Questions are:

1. I want to find fields everywhere in the region
2. Electric current density induced on the PEC surface at ##x=0##
How can I solve this problem? I can solve it if there was not PEC. Wave will be reflected from PEC, right? This reflected wave will add to the wave going toward PEC, right? Will this reflected wave also affect the wave waves in region ## x<−d ##?

Delta2
Have you learned about the method of images?

## 1. What are electromagnetic plane waves from a current sheet?

Electromagnetic plane waves from a current sheet are electromagnetic waves that are generated by an oscillating electric current flowing through a thin, flat sheet of conducting material. These waves propagate outwards in a direction perpendicular to the sheet, creating a plane wavefront.

## 2. How are electromagnetic plane waves from a current sheet different from other types of electromagnetic waves?

Unlike other types of electromagnetic waves, such as spherical or cylindrical waves, electromagnetic plane waves from a current sheet have a constant amplitude and phase across the entire wavefront. They also have a constant polarization, meaning the electric and magnetic fields are always perpendicular to each other and to the direction of propagation.

## 3. What factors affect the properties of electromagnetic plane waves from a current sheet?

The properties of electromagnetic plane waves from a current sheet are affected by the frequency of the oscillating current, the distance from the current sheet, and the conductivity and thickness of the material of the sheet. These factors determine the wavelength, amplitude, and polarization of the waves.

## 4. What applications do electromagnetic plane waves from a current sheet have?

Electromagnetic plane waves from a current sheet have many applications in various fields, including telecommunications, radar, and medical imaging. They are also used in antenna design and testing, as well as in studying the behavior of electromagnetic waves in different materials and environments.

## 5. How are electromagnetic plane waves from a current sheet measured or detected?

Electromagnetic plane waves from a current sheet can be detected using specialized equipment, such as antennas or receivers, that are designed to pick up and measure electromagnetic waves. The properties of the waves can then be analyzed and studied to gain a better understanding of their behavior and potential applications.

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