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In the image above the second faint part is the answer to the question c). The answer starts with the word evidently, and I am confused why it is evident. Also, since we are considering a shell, shouldn't it be a 3D form of Delta Dirac function? Is there anything wrong with the answer?

  • $\begingroup$ It was obviously evident to the person who wrote the answer that a delta function was the way to go. The situation is spherically symmetrical and so $r$, the distance from the origin, is a suitable variable. What do you think the answer should be? $\endgroup$ – Farcher Jan 28 '17 at 7:54
  • $\begingroup$ Hint: How can you describe a constant charge distribution $\sigma$ on the $xy$-plane? $\endgroup$ – Raziman T V Jan 28 '17 at 8:23

It is evident because there is no charge anywhere except $r=R$, therefore the charge density will have a $\delta(r-R)$ to capture this. ... and it is indeed $\delta(r-R)$ because this is spherical distribution which depend on the radial coordinate only, rather than all $3$ coordinates, i.e. you are describing a surface (2d) of fixed radius which does not depend on $\theta$ and $\phi$.

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