# Lorentz Cavity in Uniformly Polarised Dielectric: Exam Question

• manofphysics
In summary, the conversation discusses a small Lorentz cavity in a uniformly polarised dielectric and the various electric fields involved. The question is raised about whether EP changes when a sphere is cut out from the polarised dielectric, and if the result is an approximation rather than an exact calculation. The possibility of EL compensating for the change in EP is also mentioned.
manofphysics
I just have a small question regarding lorentz cavity:

Refer to a small lorentz cavity in a uniformly polarised dielectric. as shown in fig.
$$E_{ex}$$: External electric field.
$$E_{P}$$: Electric field in the uniformly polarised dielectric (when sphere has NOT been cut out)
$$E_{L}$$:Electric field due to surface charge on cavity
$$E_{near}$$:Field due to dipoles inside cavity.

Now, $$E=E_{ex}+E_{P}+E_{L}+E_{near}$$

But, does not $$E_{P}$$ change if we cut out a sphere from the polarised dielectric?
Is it that we are neglecting the small change in $$E_{P}$$ due to cut out sphere and our result is an useful approximation, but not exact?

Please, any help will be appreciated. I need to understand this for my term exam.

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I'm not sure, but offhand: If you form the cavity adiabatically, then EL would compensate for the change in EP, wouldn't it? So I suspect that's the approximation involved.

Thank you for your question. First, let's briefly review the concept of a Lorentz cavity in a uniformly polarised dielectric. A Lorentz cavity is a small empty space within a polarised dielectric material. When an external electric field, E_{ex}, is applied, it induces a polarisation, P, within the dielectric material. This polarisation creates an internal electric field, E_{P}, which opposes the external field. In addition, there may be a surface charge on the walls of the cavity, which contributes to the overall electric field, E_{L}. Finally, there may be dipoles inside the cavity which also contribute to the electric field, E_{near}.

Now, to address your question, yes, cutting out a sphere from the polarised dielectric will change the electric field, E_{P}. This is because the polarisation within the dielectric is no longer uniform since there is now a void in the material. However, the change in E_{P} may be small and can be neglected in some cases. This is because the size of the sphere and the distance from the cavity may affect the magnitude of the change in E_{P}. In other words, the closer the sphere is to the cavity, the bigger the change in E_{P} will be.

In most cases, we can neglect this small change and use the simplified equation, E=E_{ex}+E_{P}+E_{L}+E_{near}. This is an approximation, but it is a useful one in many situations. However, if you require a more precise calculation, you may need to take into account the change in E_{P} due to the cut-out sphere.

I hope this helps clarify the concept for your exam. It's important to understand the underlying principles and assumptions when using equations in science. Good luck on your exam!

## 1. What is a Lorentz cavity?

A Lorentz cavity is a type of electromagnetic cavity, which is a space that is enclosed by conducting walls and can support standing electromagnetic waves. In a Lorentz cavity, the walls are made of a uniformly polarised dielectric material, which means that the electric field within the material is aligned in a specific direction.

## 2. How does a Lorentz cavity differ from other types of electromagnetic cavities?

A Lorentz cavity differs from other types of electromagnetic cavities mainly in the material used for its walls. In other cavities, the walls may be made of conducting materials or dielectric materials with random electric field orientations, whereas in a Lorentz cavity, the walls are made of a uniformly polarised dielectric material.

## 3. What are the applications of a Lorentz cavity?

A Lorentz cavity has various applications in the field of electromagnetism. It is commonly used in research and experiments related to electromagnetic fields and waves, such as studying the behaviour of waves in different materials, or as a component in devices like filters and oscillators.

## 4. How is a Lorentz cavity formed?

A Lorentz cavity is formed by creating an enclosed space with walls made of a uniformly polarised dielectric material. This can be achieved by shaping the material into a specific geometric shape, such as a rectangular or cylindrical cavity, or by coating the walls of an existing cavity with the material.

## 5. What is the significance of the term "uniformly polarised" in a Lorentz cavity?

The term "uniformly polarised" refers to the fact that the electric field within the dielectric material is aligned in a specific direction. This is important in a Lorentz cavity as it allows for the creation of standing waves with a specific polarization, which can be useful in various applications.

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