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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