- #1
Sparky_
- 227
- 5
I do not understand the following from Griffiths’ Electrodynamics – page 424 Equation 10.21.
[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_
[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_