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  GR8677 #11
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Verbatim question for GR8677 #11
Electromagnetism}Vector Calculus

There are two identities from vector calculus one has to know by heart. The one directly applicable to this problem is:

Plug in the equation given in the problem to the identity above to get 0.

(The other identity, not quite as useful for this problem, but perhaps useful for subsequent problems, is: \nabla\times(\nabla f))

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2012-09-29 12:56:20
I solved it using Maxwell's equations. The given equation is Ampere's law in differential form. You can see the electric current term J in there. This current term is enabled by the fact that there are electric monopoles. Monopoles are allowed to exist if \nabla . D \neq 0. Only (A) has that property. If you can remember this, this method is at least as quick as using the vector identity mentioned by Yosun.NEC
pam d
2011-09-23 19:46:58
Just to be clear for people that might be foggy on vector calc, the answer is (A) for reasons already explained.NEC
2008-10-29 14:52:17
The identity didn't show up, so here it is in words:

The divergence of the curl is always zero.
2007-10-30 22:58:19
Left out an = 0 in that last part. Typo Alert!

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