Vector potential in cavity of arbitrary shape

In summary, a vector potential is a physical quantity used to describe the magnetic field in a region of space. It is calculated by solving Maxwell's equations and has various applications in physics and engineering. The shape of the cavity affects the vector potential, and limitations include assuming a static field and potential inaccuracies in complex shapes.
  • #1
Tianwu Zang
11
0
we know that vector potential in a resonator satisfies the equation [tex]\int[/tex][tex]A[/tex]([tex]\lambda[/tex])[tex]A[/tex][tex]^{*}[/tex]([tex]\lambda[/tex][tex]^{'}[/tex])[tex]d[/tex][tex]V[/tex]=[tex]4[/tex][tex]\pi[/tex]c[tex]^{2}[/tex][tex]\delta_{\lambda\lambda[/tex][tex]^{'}[/tex]
So how about in cavity of arbitrary shape? Does this equation still valid?
Thanks!
 
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  • #2
The equation represents the orthogonality of modes of different frequencies.
It would hold in a cavity of any shape, but the functions A would be harder to find.
 

Related to Vector potential in cavity of arbitrary shape

1. What is a vector potential in the cavity of an arbitrary shape?

A vector potential is a physical quantity used in electromagnetism to describe the magnetic field in a region of space. In the context of a cavity of arbitrary shape, it represents the vector field that describes the magnetic potential energy of the cavity.

2. How is the vector potential calculated in a cavity of arbitrary shape?

The vector potential in a cavity of arbitrary shape is calculated by solving the Maxwell's equations, which are a set of partial differential equations that describe the behavior of electromagnetic fields. This can be done analytically or numerically using computational methods.

3. What are the applications of vector potential in the cavity of an arbitrary shape?

The vector potential in a cavity of arbitrary shape has various applications in physics and engineering. It is used in the design of antennas, resonators, and other electromagnetic devices. It is also used in the study of quantum mechanics and in the analysis of electromagnetic scattering and diffraction.

4. How does the shape of the cavity affect the vector potential?

The shape of the cavity has a significant impact on the vector potential. In a cavity of arbitrary shape, the vector potential is influenced by the geometry and material properties of the cavity. This results in a unique vector potential for each different shape of the cavity.

5. Are there any limitations to using vector potential in the cavity of arbitrary shape?

One limitation of using vector potential in a cavity of arbitrary shape is that it assumes a static field and does not take into account time-dependent effects. Additionally, the accuracy of the vector potential calculation may vary depending on the complexity of the cavity's shape and the approximations used in the calculation.

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