# Pulsed Point Dipole

1. Feb 11, 2010

### keniwas

In Jackson's E&M book, he talks about using the following charge and current densities to demonstrate causality in the coulomb gauge.

$$\rho (\vec{r},t)=\delta(x)\delta(y)\delta'(z)\delta(t)$$
$$\vec{J}(\vec{r},t})=\delta(x)\delta(y)\delta(z)\delta'(t)\hat{z}$$

since they represent a point dipole flashing on and off at time t=0. I understand the 'flashing' aspect since the densities are only non-zero only at t=0. What I don't understand is why this represents a point dipole... why is the $$\delta'(z)$$ primed in the charge density? and likewise with the $$\delta'(t)$$ in the current?

Any thoughts?