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ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on December 31, 2009, 05:55:03 AM



Title: GR8677.011
Post by: conantee on December 31, 2009, 05:55:03 AM
11. Which of the following equations is a consequence of the equation \nabla \times \vec{H} = \dot{\vec{D}} + \vec{J} ?
(A) \nabla \cdot (\dot{\vec{D}} + \vec{J}) = 0
(B)  \nabla \times (\dot{\vec{D}} + \vec{J}) = 0
(C)  \nabla ( \dot{\vec{D}} \cdot \vec{J} ) = 0
(D) \dot{\vec{D}} + \vec{J} = 0
(E) \dot{\vec{D}} \cdot \vec{J} = 0


Title: Re: GR8677.011
Post by: conantee on December 31, 2009, 06:05:28 AM
If you still remember properties of div and curls, this problem is easy. However, suppose you forgot almost everything, use your intuition.

First, the given information is the sum of two quantities, it is unlikely that the result will turn to the dot product. So, (C) and (E) is irrelevant.

Next, (D) is too naive. How can we conclude that the sum of two quantities is zero? Don't forget that  \vec{H} is arbitary, so its curl should be arbitary.

Now, plugging values of \dot{\vec{D}} + \vec{J} into choice (A) and (B), we have to make decision between div of curl and curl of curl. Now you can make a guess. According to vector calculus, though, curl of curl piles up to a lot of terms like triple products, while div of curl gives zero.

The correct answer is then (A). 60 of 100 people got the correct answer.