Question regarding Helmoltz equation

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In summary, the Helmholtz equation is a partial differential equation that describes the relationship between time-independent electromagnetic fields and their sources. It is named after the German physicist Hermann von Helmholtz who first derived it. The equation has two main components: the Laplacian operator and the wave number, which together define the behavior of electromagnetic fields in a given system. It can be derived from Maxwell's equations and is used in a wide range of applications in fields such as optics, acoustics, and electromagnetics.
  • #1
maverick280857
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Hi,

I have the following question regarding the Helmoltz equation in the context of a Transverse Magnetic wave in a waveguide:

[tex]\nabla_{t}^{2}E_z + h^2E_z = 0[/tex]

Question: Is [itex]h[/itex] always real?

([itex]\nabla^{2}_{t}[/itex] denotes the transverse Laplacian operator)

Thanks.
 
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  • #2
In a wave guide h is almost always real. It must be real for a wave to propagate.
If the frequency is below the critical frequency, the wave is rapidly attenuated, as
exp[-(Im h)x].
 
  • #3
Thanks clem.
 

1. What is the Helmholtz equation?

The Helmholtz equation is a partial differential equation that describes the relationship between time-independent electromagnetic fields and their sources. It is named after the German physicist Hermann von Helmholtz who first derived it.

2. What is the significance of the Helmholtz equation?

The Helmholtz equation is a fundamental equation in electromagnetics and is used to solve a wide range of problems in physics and engineering, such as calculating the electric and magnetic fields around different objects or analyzing the propagation of electromagnetic waves.

3. What are the main components of the Helmholtz equation?

The Helmholtz equation has two main components: the Laplacian operator, which describes the spatial variation of a field, and the wave number, which represents the frequency of the field. Together, these components define the behavior of electromagnetic fields in a given system.

4. How is the Helmholtz equation derived?

The Helmholtz equation can be derived from Maxwell's equations, which are a set of fundamental equations that describe the behavior of electric and magnetic fields. By taking the divergence and curl of Maxwell's equations, the Helmholtz equation can be derived in its standard form.

5. What are some applications of the Helmholtz equation?

The Helmholtz equation has numerous applications in fields such as optics, acoustics, and electromagnetics. It is used to analyze and design antennas, calculate the propagation of electromagnetic waves in communication systems, and simulate the behavior of acoustic waves in medical imaging. It is also used in the study of light and sound waves in physics and engineering research.

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