Absolute potential from sphere.

[dada130500015]

Homework Statement

A conducting sphere of 5-cm radius has a surface charge density of 1 pC/m^2. If the medium of relative permittivity is 2. How can we find the absolute potential at a distance of 3m from the center of the sphere?

Homework Equations

V=Q/4∏εr

The Attempt at a Solution

In this case, i make r=3, and then sub to formula. Is that right??

 

[KilUrB]

The charge caused by the sphere, if you integrated over the surface of the sphere, would be 4*pi*r^2*1pC/m^2, where r=0.03m. Which equals pi/100 pC. Really, just the surface area of the sphere times the charge density.
Plugging this charge into the equation as "Q", with ε=2*8.85*10^-12, r=3m, we get:
(0.0314159)*10^-12/(3*4*pi*8.85*2*10^-12)= 47.0809*10^-6V or 47.0809uV. Which is the answer given in your book, assuming you're using the 5th edition of Electromagnetics with Applications.