#### fluidistic

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**1. The problem statement, all variables and given/known data**

In electrostatics it's useful to have ##\rho (\vec x )## written with Dirac's delta so that we can know the total charge by integrating the charge distribution over a region of space.

Many problems/situations deal with point charges. In Cartesian coordinates for example, ##\rho (\vec x ) = q \delta (x+3) \delta (y ) \delta (z)## means there's a charge q situated at (-3,0,0).

My question is, how do you write up the charge distribution of a point charge in spherical coordinates ##(r, \theta , \phi )## when the charge lies over the z-axis? (or at the origin for example).

Because in such a coordinate system, the angle "phi" is not well defined for the z-axis. And at the origin both phi and theta are not well defined. So I don't know how to write the charge distribution in such cases.

Thank you!