Gauss Law: Dielectric Homework - Find Electric Field and Polarization Charge

[roporte]

Homework Statement

A positive charge q is in the center of an espheric hole of radius R inside a dielectric material with constant Ke. Find the electric field module inside the dielectric in a point very near to the hole surface and the polarization charge over the surface.

Homework Equations

Gauss Law, Equations of capacitors.

The Attempt at a Solution

I try to build a gaussian surface in which i can apply gauss law, but i didn't find the way to get only one indeterminant (E for example, or qp)

Thank you very much for your help!

 

[Jhero]

Hello,

To solve this problem, you can use Gauss's Law to find the electric field inside the dielectric material. The electric field inside the dielectric, E, can be related to the charge density, ρ, by the equation E = ρ/ε, where ε is the permittivity of the dielectric material.

To find the electric field near the hole surface, you can use a Gaussian surface in the shape of a cylinder with the axis passing through the center of the hole. The radius of the cylinder should be slightly larger than R, the radius of the hole. This way, you will only have one unknown variable, the electric field, in the equation.

To find the polarization charge over the surface, you can use the equation Q = εAΔV, where Q is the total charge, A is the area of the surface, and ΔV is the potential difference between the inside and outside of the dielectric material.

I hope this helps! Let me know if you have any further questions.