Deriving electromagnetic fieldfor point charge

AI Thread Summary
The discussion revolves around the derivation of the electromagnetic field for point charges as presented in Griffith's "Introduction to Electrodynamics." The user initially expresses confusion over a missing minus sign in a specific equation related to the triple cross product rule. After further contemplation, the user realizes the error was due to neglecting the minus sign in the application of the triple cross product. This highlights the importance of careful attention to detail in mathematical derivations. The conversation concludes with the user acknowledging the oversight and resolving the issue.
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Hi all,

I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437).

I'm missing minus sign somewhere:

The book says that:\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla tr)+\vec{v}-\vec{v}(\vec{v}\cdot\nabla tr)-\vec{n}\times(\vec{a}\times \nabla tr)+\vec{v}\times (\vec{v}\times \nabla tr)

Using the rule for triple cross products gives:

\vec{v}+(v^{2}-\vec{n}\cdot\vec{a})\nabla tr

However is should be:

\vec{v}+(-v^{2}+\vec{n}\cdot\vec{a})\nabla tr


I'm sure I am missing something.

Thanks
 
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oh I've got it. Forgot the minus sign in the triple cross product rule :$
 
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