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Mictlantecuhtli
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I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is the unit step function) and obtained just what I expected $$\rho=\frac{Q}{\pi R^2} \delta (z) U(R-r)$$
The problem arise when I try to solve this problem in spherical coordinates because my first assumption was ##\rho=A \delta (\theta-\pi/2) U(R-r)## (note that here ##r## is not the same as in the previous paragraph) but some people include the scale factor corresponding to each variable appearing in each Dirac delta; in this case $$\rho=A \frac {\delta (\theta-\pi/2)}{r} U(R-r)$$
What's the reason for including such factor? Is there any mathematical result that support this?
The problem arise when I try to solve this problem in spherical coordinates because my first assumption was ##\rho=A \delta (\theta-\pi/2) U(R-r)## (note that here ##r## is not the same as in the previous paragraph) but some people include the scale factor corresponding to each variable appearing in each Dirac delta; in this case $$\rho=A \frac {\delta (\theta-\pi/2)}{r} U(R-r)$$
What's the reason for including such factor? Is there any mathematical result that support this?