I do not understand the following from Griffiths’ Electrodynamics – page 424 Equation 10.21.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\nabla p = \dot{p} \nabla {tr} = …

[/tex]

I’m not sure how much of this applies (I think my question is on the math) but p is the charge distribution, tr is the retarded time.

Is this an application of the chain rule?

With the gradient being a derivative with respect to spatial location (x,y,z), why is the time derivative showing up in the gradient? I initially want to say if something is dependent upon t but not on x, then its derivative with respect to x is zero.

The result looks like the chain rule applied – I don’t see why the time dependent portion shows up.

Can you help clear this up for me?

Thanks

Sparky_

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# Griffiths Electrodynamics gradient of charge distribution

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