In Jackson's E&M book, he talks about using the following charge and current densities to demonstrate causality in the coulomb gauge.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\rho (\vec{r},t)=\delta(x)\delta(y)\delta'(z)\delta(t)[/tex]

[tex]\vec{J}(\vec{r},t})=\delta(x)\delta(y)\delta(z)\delta'(t)\hat{z}[/tex]

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 [tex]\delta'(z)[/tex] primed in the charge density? and likewise with the [tex]\delta'(t)[/tex] in the current?

Any thoughts?

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# Pulsed Point Dipole

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