(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to follow a derivation in Jackson - Classical Electrodynamics

2. Relevant equations

In equation 1.58 (2nd/3rd edition) of Jackson - Classical Electrodynamics he says that by using the fact that [itex]\mathbf{\rho} \cdot (\mathbf{\rho} +\mathbf{n})/ | \mathbf{\rho +n|}^{3} = \nabla_{\rho}(1/|\mathbf{\rho}+\mathbf{n}|), [/itex] the integral [itex] \int {\mathbf{\rho} \cdot (\mathbf{\rho} +\mathbf{n})/ \rho^3 | \mathbf{\rho +n|}^{3}} [/itex] can be easily shown to be equal to to [itex] 4\pi [\itex].

3. The attempt at a solution

I can't really follow on how to solve this integral once the fact mentioned above is known. I know how to solve the integral using spherical coordinates, but from what I have seen that does not follow from what Jackson said at all. I am just curious if there is an easier to evaluate the integral using the gradient identity.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electrostatic interaction energy example (jackson)

**Physics Forums | Science Articles, Homework Help, Discussion**