Point dipole embedded in dielectric sphere

In summary, the task is to find the electric potential inside and outside a sphere with a point dipole p embedded at its center. The method of separation of variables may be used, with the embedded dipole considered as a free charge. The resulting polarization can be determined using the equation for bound charge density, which is proportional to the free charge density. The main challenge is setting up the boundary conditions, and any hints would be appreciated. The solution will involve adding the potential due to the dipole to that of the polarization.
  • #1
erogard
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Homework Statement



A point dipole p is embedded at the center of a sphere of linear dielectric material (with radius R and dielectric constant [tex] \epsilon_{r} [/tex]). Find the electric potential inside and outside the sphere.

Homework Equations


Well I'm guessing that using the method of separation of variables might be appropriate - my concern is to determine what "produces" the resulting potential. I would consider the embedded dipole as a free charge and go from there, but not sure what the resulting polarization might be.
Also: [tex] \rho_{b} = - ( \frac{ \chi_{e} }{1+\chi_{e} } ) \rho_{f} [/tex]
Bound charge density is proportional to free charge density (here the embedded dipole).

The Attempt at a Solution



I know how to proceed once I get my boundary conditions set up; but that's my problem at the moment. Any hint would be greatly appreciated.
 
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  • #2
Potential due to dipole + that of polarization?
 

FAQ: Point dipole embedded in dielectric sphere

What is a "Point dipole embedded in dielectric sphere"?

A point dipole embedded in a dielectric sphere is a physical system in which a small electric dipole (two opposite charges separated by a small distance) is placed at the center of a spherical material with dielectric properties (ability to resist electric fields). This system is commonly used in theoretical models to study the behavior of electric fields in materials.

How does a point dipole embedded in a dielectric sphere affect the surrounding electric field?

The presence of the point dipole in the dielectric sphere modifies the electric field in its immediate surroundings. The electric field lines will be distorted and the strength of the electric field will be different than if the dipole was not present. This is due to the interaction between the dipole and the dielectric material.

What factors affect the strength of the electric field in a point dipole embedded in a dielectric sphere?

The strength of the electric field in this system is affected by several factors, including the size and orientation of the dipole, the dielectric constant of the sphere, and the distance between the dipole and the surface of the sphere. In general, the closer the dipole is to the surface of the sphere, the stronger the electric field will be.

How is the behavior of a point dipole embedded in a dielectric sphere described mathematically?

The behavior of this system can be described mathematically using the concept of polarization, which measures the ability of a material to become electrically polarized in response to an applied electric field. The equations used to describe the electric field in this system involve the dipole moment of the dipole, the dielectric constant of the sphere, and the distance between the dipole and the surface of the sphere.

What applications does the study of point dipoles embedded in dielectric spheres have?

The study of point dipoles in dielectric spheres has applications in various fields such as material science, nanotechnology, and biophysics. It can help understand the behavior of electric fields in different materials and can also be used to design and optimize devices such as capacitors, sensors, and biological membranes.

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