Electrostatic field of a sphere

[gebhaard]

Homework Statement

What is the electrostatic field of a non-conductive sphere (it's radius is R) which has a density charge distribution inside? ρ0 and R are parameters.

Relevant Equations

Gauss' law

What is the electrostatic field of a non-conductive sphere (it's radius is R) which has a

density charge distribution inside? ρ0 and R are parameters.

I started solving this with Gauss's law:

then:

Solving the integral:

This means the electrostatic field of the sphere in r is:

Can you check if is this correct? If it isn't, what is the problem?
Thanks.

 

[PeroK]

Can you not simplify that answer? Also, the electric field is a vector.

 

[kuruman]

Also, there are two regions in space with different functional dependence for the field, $r'<R$ and $r' \geq R$. You found the field in the former but not the latter.