A sphere of radius R=0.0850 m is made up of insulating material and has a spherically symmetric charge distribution. The radial component of the electric field inside the sphere is given by:
Er= (-5.20E4) r3, for r ≤ R,
where Er is in N/C when r is in meters and r is the distance from the center of the sphere.
What is the total charge Q on the entire sphere? (Hint: Gauss's Law.)
[tex]\oint E\bullet dA [/tex] =Qencl / epsilon0
The Attempt at a Solution
I tried to set up a triple integral in spherical coords integrating -5.2E4 [tex]\rho[/tex]3[tex]\rho[/tex] sin[tex]\phi[/tex] d[tex]\rho[/tex] d[tex]\phi[/tex]d[tex]\theta[/tex]
(btw, thats supposed to be rho cubed times rho)
from 0<=[tex]\rho[/tex]<=.085, 0<=[tex]\theta[/tex]<=2pi, and 0<=[tex]\phi[/tex]<=pi
When I calculate this and multiply by epsilon, I get: -2.56E-12
which is a power of 10 off from the given answer which is: -2.56E-11
For some reason though, I feel like this is a coincidence and I'm missing something more than a power of ten somewhere. So, does my work seem to be right? If so where am I missing a power of 10 at? And also, I'm thinking there is an easier way to do this problem other than integrating so any insight into that would be great!