- #1

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I tried to calculate the electric field produced by a sphere of uniform charge using this formula:

[tex]

E(r)=\frac{1}{4\pi\epsilon_0} \iiint\rho(r') \frac{r-r'}{|r-r'|^3} d^3r'

[/tex]

I know I could could use gauss's law but I wanted to do it directly just to see. I tried to do it in cartesian coordinates. Well as you probably know the math gets super tedious for this problem. So what I did is I tried to simplify the problem in lower dimensions. I thought about doing a circle of uniform charge but instead I went for the one-dimensional case of a line charge on the x-axis from -R to R. I came up with this formula to solve it.

[tex]

E(x)=\frac{\lambda}{4\pi\epsilon_0} \int_{-R}^{R} \frac{x-x'}{|x-x'|^3} dx'

[/tex]

After I solved this problem I found something unusual. As I approached R from the x>R side the value of E became infinity. When I know for a uniform sphere it becomes a finite value. Does this make sense to anybody?