Derivative of a vector expression?

  • Thread starter quarky2001
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  • #1
quarky2001
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I'm trying to find the time derivative of the following function, where E is a constant, spatially uniform vector field, and B is as well, but B varies with time.

[tex]
\frac{d}{dt}\left(\frac{\vec{E}\times\vec{B}}{B^2}\right)
[/tex]

Remembering that B is time dependent and E is not, I've calculated the derivative of this as (where a dot above the letter indicates a time derivative):

[tex]
\frac{1}{B^4}\left[B^2(\vec{E}\times\dot{\vec{B}})-2B\dot{B}(\vec{E}\times\vec{B})\right]
[/tex]

Can anyone tell me if this is correct?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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That looks fine to me, assuming you mean a dot product between B and its derivative.
 
  • #3
quarky2001
34
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Whoops, forgot that! Thanks for checking it though. It's a shame it doesn't simplify more, but so long as it's correct I'm fine with it.
 

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