Dielectric sphere in point charge electric field

In summary, the conversation discusses the possibility of computing the potential inside and outside a dielectric sphere with permittivity ε1 when a point charge q with permittivity ε2 is placed outside the sphere. The person has tried using Legendre polynomials, but obtained an infinite sum that cannot be interpreted as images. It is concluded that this problem cannot be solved using methods of images. However, it is mentioned that images do work, but there are infinitely many of them. The conversation ends with the realization that the problem can only be solved in terms of an infinite sum, similar to how sin x is calculated.
  • #1
paweld
255
0
I'm interested if it's possible to compute potential inside and outside
dielectric sphere (with permittivity [tex]\varepsilon_1 [/tex]) which is
placed in field of point charge q lying outside the sphere where
permittivity is [tex]\varepsilon_2 [/tex]. I've tried to solve it
using Legendre polynomilas but I obtain infinite sum which
I cannot interpretate as images (maybe I made a mistake).
So this problem cannot be solve using methods of images?
 
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  • #2
Images won't work. Your LP sum is the standard solution.
 
  • #3
Images work, but there are infinitly many of them!
 
  • #4
Thanks for answers. It's quite strange that such apparently simple
problem has only solution in terms of infinite sum.
 
  • #5
sin x is also calculated by an infinite sum.
 
  • #6
indeed, for computer it doesn't matter
 

What is a dielectric sphere?

A dielectric sphere is a spherical object made of an insulating material, such as rubber or glass, that does not conduct electricity.

What is a point charge electric field?

A point charge electric field is a type of electric field that is created by a single, stationary charge. It is a theoretical concept used in physics to study the behavior of electric fields.

How does a dielectric sphere behave in a point charge electric field?

A dielectric sphere in a point charge electric field will experience a force due to the electric field. The dielectric sphere will also experience a polarization, where the molecules within the sphere will align in response to the electric field.

What is the relationship between the electric field and the polarization of a dielectric sphere?

The electric field and the polarization of a dielectric sphere are directly related. The polarization is proportional to the electric field and can be calculated using the dielectric constant of the material and the electric field strength.

How does the presence of a dielectric sphere affect the electric field around a point charge?

The presence of a dielectric sphere in a point charge electric field will result in a decrease in the electric field strength. This is due to the polarization of the dielectric material, which creates an opposing electric field that cancels out some of the original field.

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