# Calculating size of charge distribution with a known electric field

## Homework Statement

A complicated distribution of 10 protron produces a radially symmetric electric field given by,

E(r) = (10*charge_of_proton/4pi*epsilon_0)*(1/r^2 + 100/r^4)*r_hat

Give an order of magnitude estimate for the size of the charge distribution.

## The Attempt at a Solution

I thought that r could be expressed as sqrt(a^2 + z^2), "z" being the distance from the charges, and "a" being the size of the radius of the charge distribution. With this method, I'm having trouble finding the right values for "z" and E(r) that will help me calculate "a". Basically, we know what the electric field looks like, so we should be able to give a rough estimate on the size of the charge distribution. Could anyone point me in the right direction? Any help would be appreciated.

You might try using Gauss' Law to calculate the total charge enclosed by a concentric spherical gaussian surface of radius $r$. You know that the total charge of the distribution is 10 times the charge of the proton, so you can then calculate the minimum radius $r$ for which your Gaussian encloses that amount of charge.