What is the Magnitude of the Electric Field Inside and Outside a Charged Sphere?

[musicman05]

Homework Statement

A solid sphere of radius 40.0 cm has a total positive charge of 46.0 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field:

10.0 cm from the center of the sphere
40.0 cm from the center of the sphere
60.0 cm from the center of the sphere

Homework Equations

E=kq/r^2

The Attempt at a Solution

8.99e9*46e6/60cm=6.892333333e15

 

[Snazzy]

Let's call the charge enclosed by a sphere of radius r (with r < R) Q', and the charge of the entire sphere, Q.

The ratio of the charges is thus $$\frac{Q'}{Q}=\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}$$

or:

$$Q'=Q\frac{r^3}{R^3}$$

Using this, and the fact that $$\int \vec{E}.\vec{da}=\frac{q}{\epsilon _0}$$ from Gauss's Law.

You can calculate the electric field at any point within the sphere.