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## Homework Statement

a) A charge q

_{1}= q is at

**r'**= -D

_{1}**i**, and a charge q

_{2}= -3q is at

**r'**= D

_{2}**i**. Find an expression for the volume charge density p(

**r**).

b) An infinitely long wire along the z-axis has a uniform linear charge density [tex]\lambda[/tex]. Find an expression for the volume charge density p(

**r**) in cylindrical coordinates.

## Homework Equations

[tex]\int[/tex][tex]\delta[/tex](x) dx = 1

## The Attempt at a Solution

a) I'm not sure how to format my solution for the question, but I came up with this:

p(

**r**) = [[tex]\delta[/tex](

**r**- D

**i**)(-3q) + [tex]\delta[/tex](

**r**+ D

**i**)(q)]

b) I can't figure out how to do this with cylindrical coordinates. With Cartesian coordinates I came up with this:

p(x,y,z) = [tex]\delta[/tex](x)[tex]\delta[/tex](y)[tex]\lambda[/tex]

When I try with cylindrical coordinates, I realize that r must equal zero, so I know [tex]\delta[/tex](r) would be part of the expression; however, [tex]\theta[/tex] can be any value, as can z. That results in this:

p(r,[tex]\theta[/tex],z) = [tex]\delta[/tex](r)[tex]\lambda[/tex]

which has incorrect units for volume charge density.

Any help on this question is greatly appreciated!