# Definition:Dipole

## Definition

Let $\phi \in \map \DD \R$ be a test function.

Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution.

Then for any $\phi$ the distributional derivative of $\delta$ is known as the dipole and is given by:

$\ds \map {\delta'} \phi = - \map {\phi'} 0$