A point charge inside infinite medium of dielectric

[Ready2GoXtr]

A point charge inside infinite dielectric material

1. The problem statement, all variables and given known data
A point charge is an infinite medium of dielectric material having a relative permittivity \epsilon_r. <--- epsilon(sub r). Find the electric field vector and the potential function at any point in space, assuming that the potential is zero volts at infinity.

Homework Equations

D = \epsilon * E + P
P = \epsilon₀ * \chi_e vector E
\epsilon[\tex] = \epsilon&lt;sub&gt;0&lt;/sub&gt; * \epsilon&lt;sub&gt;r&lt;/sub&gt;<br /> \chi&lt;sub&gt;e&lt;/sub&gt; = \epsilon&lt;sub&gt;r&lt;/sub&gt; - 1<br /> <br /> <br /> well its not letting me put it in right so I am going to enter them in with () next to them <br /> D(vector) = epsilon*E(vector) + P(vector)<br /> P(vector) = epsilon(sub 0)*chi(sub e)*E(vector)<br /> epsilon = epsilon(sub 0)*epsilon(sub r)<br /> chi(sub e) = epsilon(sub r) - 1<br /> Electric Field of Point Charge = k*q/r^2<br /> Electric Field of Sphere = q/(4*pi*epsilon(sub0)*r^2)<br /> <br /> <h2>The Attempt at a Solution</h2><br /> Im not quiet sure what my first step would be. I would think that a point charge inside a dielectric medium would have a reduced electric field, but it is infinite so wouldn&#039;t its electric field be nothing?

 

[gabbagabbahey]

Just use Gauss' Law for \textbf{D}...can you think of a Gaussian surface that will exploit the symmetry present?

 

[Ready2GoXtr]

what do you mean by exploit?

 

[gabbagabbahey]

"Exploit" is just another word for "use"

 

[Ready2GoXtr]

I feel that a sphere represents a good shape.

 

[gabbagabbahey]

I feel that a sphere represents a good shape.

Okay, but why? And where will the center of the sphere be?

 

[Ready2GoXtr]

The center of the sphere will be located on the point charge

 

[Ready2GoXtr]

so would my answer just be q/(4*pi*epsilon(sub0)*r^2)
?

 

[gabbagabbahey]

Not quite...What is Gauss' Law in terms of \textbf{D}? Do you see why Gauss' Law in terms of \textbf{E} isn't helpful here?