Introduction to Electrodynamics · Problem 1.39

Vector Analysis — David J. Griffiths

Physics · divergence-theorem-spherical

Problem

(a) Check the divergence theorem for the function

\mathbf{v}_1 = r^2 \hat{\mathbf{r}}

, using as your volume the sphere of radius

R

, centered at the origin. (b) Do the same for

\mathbf{v}_2 = (1/r^2)\hat{\mathbf{r}}

. (If the answer surprises you, look back at Prob. 1.16.)