# Homework Help: Electric field of a point charge inside a sphere

1. May 5, 2014

### melodyyyylwy

1. The problem statement, all variables and given/known data

(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 Er(r) inside the sphere as a function of r < R.
Using the fact that $\underline{∇}$$\cdot$E(r) = $\frac{1}{r^2}$$\frac{∂}{∂r}$(r2Er(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 Er (considered in part (a)).

2. Relevant equations

3. 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?

2. May 5, 2014

### Simon Bridge

Superposition principle.