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## Homework Statement

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.)

## Homework Equations

Gauss's law:

[tex]\oint E\bullet dA [/tex] =Q

_{encl}/ epsilon

_{0}

## 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!

Thanks!