Electric field of a point charge inside a sphere

[melodyyyylwy]

Homework Statement

(a)Consider a charged sphere of radius R centred at the origin with the spherically symmetric charge density ρ(r) = ρ₀(r4/R4) where ρ₀ is a constant and r is the radial coordinate.
Find the charge dQ₀ contained in a spherical shell of radius r₀ < R and infinitesimal thickness dr₀.
Hence find the charge Q(r) contained inside the sphere as a function of
r < R.
Using Gauss’s law in integral form, determine the magnitude of the radial electric field E_r(r) inside the sphere as a function of r < R.
Using the fact that \underline{∇}\cdotE(r) = \frac{1}{r^2}\frac{∂}{∂r}(r²E_r(r)) in this case, verify Gauss’s law in
differential form at a general point inside the sphere.

(b) A positive point charge Q is added to a point P₀ with position vector R₀ with components (1, 1, 1) inside a sphere with the same charge density as in part
(a) apart from the charge Q. Calculate the vector electric field E(r) at a point
P with position vector r with components (1, 2, 1) inside the sphere in terms
of the unit vectors \widehat{x}, \widehat{y}, \widehat{z} and Q and E_r (considered in part (a)).

Homework Equations

The Attempt at a Solution

i have done part b of the question already. i am just not quite sure how to deal with a point charge inside a sphere with charge density. Do i just add up the two field?

 

[Simon Bridge]

Superposition principle.