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GR8677 #11
Problem
 GREPhysics.NET Official Solution Alternate Solutions

Electromagnetism$\Rightarrow$}Vector Calculus

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

$\nabla \cdot (\nabla \times \vec{H})=0
$

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: $\nabla\times(\nabla f)$)

Alternate Solutions
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 nakib2012-09-29 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.Reply to this comment pam d2011-09-23 19:46:58 Just to be clear for people that might be foggy on vector calc, the answer is (A) for reasons already explained.Reply to this comment casanovo2008-10-29 14:52:17 The identity didn't show up, so here it is in words: The divergence of the curl is always zero.Reply to this comment Furious2007-10-30 22:58:19 Left out an = 0 in that last part. Reply to this comment

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