# Phase relation between current and electromagnetic field generated

• amir11
In summary, the phase relation between a current source and the generated electromagnetic field components can be complex and depends on various factors such as the medium properties, eigenvalues, and spatial phase shift. In general, the electric field may lead the current by 90 degrees at the source point, but as the fields propagate there may be additional phase shifts. In the case of a waveguide, the superposition of reflections can further complicate the phase relation. It is difficult to determine a general rule for this and may require detailed analysis.
amir11
Dear ForumersI am having a bit problem understanding the phase relation between current source and the generated eletromagnetic field components.
Assume a very small current element( a very small current running in direction x)(essentially an electric dipole) in a non-homogenous loss periodic medium. the only knowledge about the medium is the mu and epsilon profile plus eigenvalues of the medium. The structure is like a waveguide so most of the radiation is expected to couple one of the eigenvalues. what is the phase relation between the generated electromagnetic field(dominant eigenvalue) and the driving current?(assuming phasor fields). It must be somehow related to the tangental and normal electric and magnetic fields of the dominant eigenvalue.

could it be independent of the meduim, simply 1 or -1?

Best

From Maxwell's Equations, for a time-harmonic field the electric field it appears that it may lead the current by 90 degrees since the time derivative of the electric field is equal to the curl of the magnetic field and the source current. But this is only at the source point, due to the retardation of the fields, there is another phase shift that arises as the fields propagate. Let us take the z component of the electric field from a z directed point source current. The field for a unity current source is:

$$E_z = \frac{i\omega\mu}{4\pi k^2} \left[ ik - \frac{1+k^2z^2}{r^2} - \frac{3ikz^2}{r^2} + \frac{3z^2}{r^3} \right] \frac{e^{ikr}}{r^2}$$

So we find that different parts of the field are 90 degrees and 180 degrees out of phase of the current even before we take into account the spatial phase shift. As you go away from the source though, only the first term remains and you have a field that is 180 degrees out of phase plus a spatial phase shift.

So in the situation where you have a waveguide, then you have to contend with the superposition of the reflections which would make it even more difficult. But my guess is you will have a hard time determining a rule for this.

## 1. What is the phase relation between current and electromagnetic field generated?

The phase relation between current and electromagnetic field generated refers to the relationship between the two components in an electromagnetic wave. In simple terms, it describes how the current flowing through a conductor creates an electric field, which in turn creates a magnetic field, and vice versa.

## 2. How does the phase relationship affect the behavior of electromagnetic waves?

The phase relationship is crucial in determining the behavior of electromagnetic waves. It determines properties such as wavelength, frequency, and direction of propagation. It also affects how these waves interact with matter, leading to phenomena such as reflection, refraction, and diffraction.

## 3. Is the phase relationship constant for all electromagnetic waves?

No, the phase relationship can vary depending on the source of the electromagnetic waves. In general, the phase difference between the electric and magnetic fields is 90 degrees for most sources, but it can be different for some types of waves, such as circularly polarized waves.

## 4. How is the phase relationship between current and electromagnetic field measured?

The phase relationship can be measured using an oscilloscope or a vector network analyzer. These instruments allow for the visualization and analysis of the electric and magnetic fields of an electromagnetic wave, allowing for the determination of the phase difference between them.

## 5. What is the significance of the phase relationship in practical applications?

The phase relationship is essential in many practical applications, such as wireless communication, radar, and medical imaging. Understanding and controlling the phase relationship allows for the manipulation and optimization of electromagnetic waves for specific purposes, leading to advancements in technology and science.

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