The problem involves determining the charge distribution p(rho) from a given electric field E(r) using Gauss' law. The electric field is expressed in terms of a constant and an exponential decay function, and the tasks include finding the total charge and integrating the charge distribution.
The discussion is ongoing, with participants providing partial calculations and seeking clarification on specific steps. Some guidance has been offered regarding the divergence calculation and the integration limits, but there is no explicit consensus on the correct approach yet.
Participants are reminded to show their work in accordance with forum rules, and there is a focus on ensuring that the calculations align with the appropriate mathematical frameworks for spherical coordinates.
vela said:According to the forum rules, you need to show some effort at working the problem yourself before you can receive help.
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.jajay504 said: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.
It's not a surface; it's a volume. What is dV in spherical coordinates? What limits should you be integrating over?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