Dielectric Image Charges. Need

In summary, the conversation discusses finding the potential outside of a dielectric half-space with a point charge at a distance d. The first question is about the equation satisfied by the potential away from the point charge and the boundary conditions at the dielectric surface. The second question involves finding an image charge in the dielectric slab to satisfy the boundary conditions and determining the potential outside the dielectric. The hint suggests that as the dielectric constant approaches infinity, the result should match that of a charge next to an infinite conducting half-space. The equations used for the potential and the method for obtaining the boundary conditions are also mentioned.
  • #1
Einsteinium1
1
0
A point charge q is a distance d from a dielectric half-space (z < 0). We will
solve for the potential outside of the dielectric, in the region z > 0.

(a) Away from the point charge, what equation does V satisfy? Find the boundary conditions at the dielectric surface.

(b) Find an image charge in the dielectric slab that allows you to satisfy the
boundary conditions. What is the potential V outside the dielectric?

(Hint: as [tex]\epsilon[/tex] -> [tex]\infty[/tex], you should recover the result for a charge next to an infinite conducting half-space.

I'm pretty lost with this question. Any hints starting the problem would be very helpful. Thank you.
 
Physics news on Phys.org
  • #2
(a) is pretty simple. In free space, what equation do you use for the potential?

You can get the BC's from Gauss's law and Faraday's law for the electric field. Then convert those to BC's for the potential.
 

1. What is a dielectric image charge?

A dielectric image charge is an imaginary charge that is induced on the surface of a dielectric material when it is placed in an external electric field. It is created due to the polarization of the dielectric material, which leads to the formation of an electric dipole.

2. How is a dielectric image charge different from a regular charge?

A dielectric image charge is different from a regular charge in that it is an imaginary charge and does not actually exist. It is only a mathematical construct used to simplify the analysis of electric fields in the presence of dielectric materials. Regular charges, on the other hand, are physical entities with a specific magnitude and location.

3. What factors influence the magnitude of a dielectric image charge?

The magnitude of a dielectric image charge is influenced by several factors, including the magnitude and location of the external electric field, the permittivity of the dielectric material, and the geometry of the dielectric material.

4. How is the presence of dielectric image charges accounted for in electric field calculations?

In electric field calculations, the presence of dielectric image charges is accounted for by using the concept of electric flux density. This allows for the inclusion of both the induced image charges and the external charges in the calculation of the electric field.

5. Can dielectric image charges be physically measured?

No, dielectric image charges cannot be physically measured as they are only a mathematical construct. However, their effects can be observed and measured through the changes in the electric field and potential in the presence of dielectric materials.

Similar threads

  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
1
Views
1K
Replies
4
Views
811
  • Advanced Physics Homework Help
Replies
3
Views
401
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
3K
  • Electromagnetism
Replies
1
Views
675
Back
Top