# Find Electric Field Around a Non-Conducting Sphere

• tuggler
In summary, the conversation discusses a non-conducting sphere with a non-uniform charge distribution and the use of Gauss' Law to find the electric field at different distances from the origin. An algebraic expression for the total charge on the sphere is given, and the question asks for the electric field within and outside the sphere. The attempted solution for part a is correct, but the solution for part 2 is incorrect and further clarification is needed.

## Homework Statement

I. A non-conducting sphere of radius a has a spherically symmetric, but non-uniform charge distribution is placed on it, given by the volume density function: p(r) = C·r, where C is a positive constant, and 0 < r < a.

a. Find an algebraic expression for the total charge Q on the sphere, in terms of the parameters C and a.

II. Use Gauss' Law to find an algebraic expression for the magnitude of the electric field at a distance R from the origin, in each of the following regions. Express your answer in terms of the following four parameters: the electrostatic constant k; the radius a of the sphere; the total charge Q on the sphere; and the radial distance R from the origin to the field point.

b. Within the insulating sphere (i.e. for R <a):

c. Outside the sphere (i.e. for R > a):

## The Attempt at a Solution

I got Q = Cpi(a^4) for part a which is correct.

For part 2 I am stuck both b and c.

I got [(KQR^4)/((a^4)(r^2))] which is incorrect.

tuggler said:
For part 2 I am stuck both b and c.

I got [(KQR^4)/((a^4)(r^2))] which is incorrect.
r is what I got with determining K. I got $$\frac{1}{4\pi \epsilon_0 r^2},$$ but I replaced the 1/4pi e_0 with K.