Dirac Delta function and Divergence

[Apple96]

Homework Statement

The Potential V(r) is given: A*e^(-lambda*r)/r, A and lambda are constants
From this potential, I have to calculate: E(r), Rho(r) -- charge density, and Q -- total charge.

Homework Equations

The Attempt at a Solution

I know that E(r) is simply minus gradient of V(r), which is lambda*A*e^(-lambda*r)/r + A*e^(-lambda*r)/r^2. And, the rho will be equal to divergence of E times emissivity constant, according to the Gauss' Law and Divergence theorem. However, I'm having trouble calculating the divergence of E(r). Apparently, I have to use the Dirac Delta Function, but I'm simply lost from here. Please help me out.

Thank you,

 

[BruceW]

hmm. Just have a go at calculating the divergence of E(r). Clearly, something slightly strange will happen at r=0. But for r>0 you can see what happens without worrying about Dirac Delta functions.