In: Physics
Consider a spherical charge distribution of radius R with a
uniform charge density ρ.
Using Gauss' Law find the electric field at distance r from the
axis where r < R.
First, consider a Gaussian sphere of radius inside the sphere of radius
Since a uniform charge density of is given, the final equation will be independent of the radius of the sphere.
Gauss's Law states that the electric flux through a symmetrical surface is equal to the enclosed charge divided by the absolute permittivity of space.
Here, to calculate , we can just use the density of charge times the volume of the charge distribution enclosed by the surface.
Evaluating , we get
Therefore, by Gauss's Law
We can see here that the electric field depends on the size of the Gaussian Surface taken, and is independent of the size of the charge distribution, provided