Sunday, 24 July 2016

homework and exercises - Divergence of frachatrr2


In David J. Griffiths's Introduction to Electrodynamics, the author gave the following problem in an exercise.



Sketch the vector function v = ˆrr2,

and compute its divergence, where ˆr := rr,r := |r|.
The answer may surprise you. Can you explain it?



I found the divergence of this function as 1x2+y2+z2

Please tell me what is the surprising thing here.



Answer



Pretty sure the question is about ˆrr2, i.e. the electric field around a point charge. Naively the divergence is zero, but properly taking into account the singularity at the origin gives a delta-distribution.



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