Introduction to Electrodynamics · Problem 1.15

Vector Analysis — David J. Griffiths

Physics · divergence

Problem

Calculate the divergence of the following vector functions: (a)

\mathbf{v}_a = x^2 \hat{\mathbf{x}} + 3xz^2 \hat{\mathbf{y}} - 2xz\,\hat{\mathbf{z}}

. (b)

\mathbf{v}_b = xy\,\hat{\mathbf{x}} + 2yz\,\hat{\mathbf{y}} + 3zx\,\hat{\mathbf{z}}

. (c)

\mathbf{v}_c = y^2 \hat{\mathbf{x}} + (2xy + z^2)\hat{\mathbf{y}} + 2yz\,\hat{\mathbf{z}}