Electrodynamic - Spherical cavity in dielectric

In summary, the conversation discusses a physics problem involving a sphere with a radius of a and permittivity of ε2 placed in a dielectric ε1. The solution to the problem is being sought when ε2 is equal to 1 (vacuum). The conversation also mentions the use of test functions and the need to consider the density of charge and field produced by these charges. The person asking for help has looked through the textbook but is struggling to find a starting point for the problem. A suggestion is given to refer to a specific section in the book for help.
  • #1
emeriska
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First, sorry if something is not totally clear, I'm translating physics term the best I can!

1. Homework Statement
A sphere or radius a of permittivity ε2 is placed in a dielectric ε1. Without the sphere, we would have E = E0. We want to find the solution to this problem when ε2 = 1 (vacuum).

Homework Equations


Seems like I'll need those test functions:
V1=-E0 + p/r3 (when r > a)
V2=-E2 (when r < a)

The Attempt at a Solution


I figured I'll need density of charge of polarization at the surface and the field produced by these charges.

So now the thing is my last electrodynamic course was a loonng time ago and I'd kinda need a head start on this one. I'm looking through the Griffith but I can't seem to find anything to help me get this problem started.

If you guys have any ideas of links that might help that'd be great! Thanks!
 
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  • #2
Since you have Griffiths, look at the section titled "Boundary Value Problems with Linear Dielectrics". In the the 3rd edition, it is section 4.4.2. There is an example problem that is similar to (but not the same as) your problem.
 
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1. What is electrodynamic in a spherical cavity?

Electrodynamic in a spherical cavity refers to the study of electric and magnetic fields within a cavity or enclosed space containing a dielectric material. This phenomenon is important in understanding the behavior of electromagnetic waves and their interactions with matter.

2. How does the shape of the cavity affect electrodynamic behavior?

The shape of the cavity can greatly impact the electrodynamic behavior within it. For example, in a spherical cavity, the electric and magnetic fields are radial, while in a cylindrical cavity, they are circumferential. The shape also affects the resonant frequencies and field distributions within the cavity.

3. What is a dielectric material and how does it influence electrodynamic behavior?

A dielectric material is an insulating material that is able to store electric charge. It is characterized by its permittivity, which is a measure of how easily it can be polarized by an electric field. In an electrodynamic system, the presence of a dielectric material can alter the distribution of electric and magnetic fields, impacting the overall behavior of the system.

4. What is the significance of studying electrodynamic in a spherical cavity?

The study of electrodynamic in a spherical cavity has many practical applications, such as in the design of antennas and microwave resonators. It also has theoretical importance in understanding the behavior of electromagnetic waves and their interactions with matter.

5. How is electrodynamic in a spherical cavity related to quantum mechanics?

Electrodynamic in a spherical cavity is closely related to quantum mechanics through the concept of quantum vacuum fluctuations. These fluctuations, caused by the constant creation and annihilation of particle-antiparticle pairs, contribute to the overall electromagnetic field within the cavity and impact its behavior. This connection between electrodynamic and quantum mechanics is important in studying and understanding both fields.

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