Question

Suppose you have a spherical volume of uniform charge density rhov extending from R=0 to R=a in free space.

a. Find the electric field everywhere in space, i.e., R≤a and R>a
b. Find the potential everywhere in space (R≤a and R>a ) with respect to zero potential at R=[infinity]. Plot your answer as a function of R.

Answer 1

To find the electric field and potential for a spherical volume of uniform charge density, use Gauss's law and the equation for electric potential, respectively.

Step-by-step explanation:

In order to find the electric field and potential for a spherical volume of uniform charge density, we need to use Gauss's law and the equation for electric potential, respectively.

a. Electric Field:

If we have a spherical volume of charge density ρv extending from R=0 to R=a, the electric field E everywhere in space is given by:

E = (1 / (4πε)) * (Q / R2)

where ε is the permittivity of free space, and Q is the total charge enclosed by the surface.

b. Potential:

The electric potential V everywhere in space is given by:

V = (1 / (4πε)) * (Q / R)

where ε is the permittivity of free space, and R is the distance from the center of the sphere.