Question

In: Physics

Consider a spherical charge distribution of radius R with a uniform charge density ρ. Using Gauss'...

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.

Expert Solution

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

genius_generous answered 2 years ago

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