E Field of Sphere: Find Magnitude at Distance .05m

[pyroknife]

Homework Statement

A nonconducting solid sphere of radius (R) .1m has uniform volume charge density (2*10^-6 C/m^3 was calculated and verified accurate). Find the magnitude of the e field at a distance (r) .05m from the sphere's center.

Homework Equations

The Attempt at a Solution

flux=E*4*pi*r^2 = Q/Eo
I calculated Q by multiplying the volume charge density by its volume (4/3)*pi*(.1^3) which got me 8.38e-9 C.

I solved for E=Q/(Eo * 4 * pi * r^2) which got me 30000 N/C. But that answer was 470 N/C. What did i do wrong?

 

[issacnewton]

you have to use the electric field inside the sphere since r=0.05 m is less than the radius
R= 0.1 m. Electric field inside the sphere at a distance r from the center is

$$E(r)=\frac{1}{4\pi \epsilon_o}\;\frac{Q}{R^3}\;\; r$$

where Q is the total charge

reference:http://www.phys.uri.edu/~gerhard/PHY204/tsl56.pdf