Find electric field inside and outside of uniformly charge sphere of radius R and q. Also, plot IEI asa function of distance r

To solve this problem, we will use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

1. Inside the Sphere (r < R):

   For r < R, the sphere can be thought of as a superposition of an infinite number of infinitesimally thin spherical shells. The electric field due to each shell at a point inside the shell is zero. Therefore, the electric field at a point inside the sphere is zero.

2. On the Surface of the Sphere (r = R):

   At the surface of the sphere, the enclosed charge is q. According to Gauss's Law, the electric field is given by E = q / (4πε₀R²), where ε₀ is the permittivity of free space.

3. Outside the Sphere (r > R):

   For r > R, the sphere behaves as if all its charge were concentrated at its center. Therefore, the electric field is given by E = q / (4πε₀r²).

To plot |E| as a function of distance r, you would have a graph with the following characteristics:

• For r < R, |E| = 0.
• At r = R, |E| jumps to q / (4πε₀R²).
• For r > R, |E| decreases as 1/r².

The plot would start at the origin (0,0), jump to q / (4πε₀R²) at r = R, and then decrease as 1/r² for r > R. The plot would be discontinuous at r = R.