Introduction to Electrodynamics · Problem 5.7

Magnetostatics — David J. Griffiths

Physics · current-density-dipole-moment

Problem

For a configuration of charges and currents confined within a volume

\mathcal{V}

, show that

\int_{\mathcal{V}} \mathbf{J}\, d\tau = d\mathbf{p}/dt, \tag{5.31}

where

\mathbf{p}

is the total dipole moment. [Hint: evaluate

\int_{\mathcal{V}} \nabla \cdot (x\mathbf{J})\, d\tau