GR8677 #80



Alternate Solutions 
nakib 20100402 09:01:27  Don't go for calculating all the answer choices for .
Eliminate C, D ~> Each term has a nonzero contribution to the div. but both terms are +ve, they can't possible cancel each other out.
Eliminate E ~> Just one term that has a nonzero contribution to the div.
Eliminate A ~> Each term has a nonzero contribution to the div. but one term has a factor of multiplied to it.
(B) is the correct choice.   senatez 20061016 20:25:28  The electric field must also be a gradient of a function (the potential). Mixed partials of the potential function must be equal.  

Comments 
nakib 20100402 09:01:27  Don't go for calculating all the answer choices for .
Eliminate C, D ~> Each term has a nonzero contribution to the div. but both terms are +ve, they can't possible cancel each other out.
Eliminate E ~> Just one term that has a nonzero contribution to the div.
Eliminate A ~> Each term has a nonzero contribution to the div. but one term has a factor of multiplied to it.
(B) is the correct choice.
neon37 20101104 04:40:24 
Its not too hard if you think about how to do it fast before hand. It might take longer to think about some other logic. Divergence is a dot product, so for terms you take . That shouldnt be too difficult. In this case it was just the second one, so it took me about 7 seconds maximum after reading the question.

  senatez 20061016 20:25:28  The electric field must also be a gradient of a function (the potential). Mixed partials of the potential function must be equal.
student2008 20081012 12:08:08 
Not necessarily. Since , you're right only in the electrostatic case, which takes place here. And in general we can't get rid of the by a gauge transformation, since the condition implies scalar ones.
Although, since there're only expressions for the electric field, we can infer that the problem electrostatic.

Prologue 20091106 21:03:53 
You can't infer that it is electrostatic, the curl is nonzero.

 

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