# Electric Fields, Flux, Gauss' Law

1. Sep 12, 2011

### jajay504

1. The problem statement, all variables and given/known data
The Electric field E produced by an unknown charge distribution p (rho) is E(r)= (constant)*((exp(-ar))/r^2)*(r_hat).
a.) Use Gauss' law in differential for to determine p(rho)
b.) Find the total charge q_tot by directly integrating p(rho), and show that it is 0.
c.) Find q_tot again, except this time use Gauss' law in integral form.
d.) Make a sketch of p(rho)

2. Relevant equations

3. The attempt at a solution

2. Sep 12, 2011

### vela

Staff Emeritus
According to the forum rules, you need to show some effort at working the problem yourself before you can receive help.

3. Sep 12, 2011

### jajay504

Hey! Sorry for that... I did some work but I got stuck.

I used divergence E = p/e0

a.) div E = (-a/r^2 - 2/r^3) * exp(-a*r) = p/e0. So I know what p is.
b.) Then I tried to integrate over p(rho) to get q_tot

q_tot = Integral [pdV]
I got --> exp(-a*r)/r^2 - 2*exp(-a*r)/r^3 = q_tot

I'm still trying to figure out what is this surface

4. Sep 12, 2011

### jajay504

Sorry for that!! I put down the work I had

5. Sep 12, 2011

### vela

Staff Emeritus
You calculated the divergence incorrectly. Look up the formula for the divergence in spherical coordinates. Your book should have a list of the various vector operators for different coordinate systems.
It's not a surface; it's a volume. What is dV in spherical coordinates? What limits should you be integrating over?