Introduction to Electrodynamics · Problem 1.49

Vector Analysis — David J. Griffiths

Physics · dirac-delta-function-3d

Problem

Evaluate the integral

J = \int_{\mathcal{V}} e^{-r} \left( \nabla \cdot \frac{\hat{\mathbf{r}}}{r^2} \right) d\tau

(where

\mathcal{V}

is a sphere of radius

R

, centered at the origin) by two different methods, as in Ex. 1.16.