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## Main Question or Discussion Point

Hello,

In my plasma physics book, poissons equation in relation to a plasma made up of electrons and protons is given as

[tex]\frac{1}{r^{2}}\frac{d}{dr}\left(r^{2}\frac{d\varphi\left(r\right)}{dr}\right) = \frac{2}{\lambda_{D}}\varphi\left(r\right)[/tex]

The solution of this equation when phi(r) tends to 0 for r tending to infinity is

[tex]\varphi\left(r\right) = \frac{e}{4\pi\epsilon_{0}r}exp\left(-\frac{\sqrt{2}r}{\lambda_{D}}\right)[/tex]

How do you get to this solution? I have tried multiplyin both sides by r^2, then integrating w.r.t. r, by parts, but I cannot get any further than that.

Regards,

Peter

In my plasma physics book, poissons equation in relation to a plasma made up of electrons and protons is given as

[tex]\frac{1}{r^{2}}\frac{d}{dr}\left(r^{2}\frac{d\varphi\left(r\right)}{dr}\right) = \frac{2}{\lambda_{D}}\varphi\left(r\right)[/tex]

The solution of this equation when phi(r) tends to 0 for r tending to infinity is

[tex]\varphi\left(r\right) = \frac{e}{4\pi\epsilon_{0}r}exp\left(-\frac{\sqrt{2}r}{\lambda_{D}}\right)[/tex]

How do you get to this solution? I have tried multiplyin both sides by r^2, then integrating w.r.t. r, by parts, but I cannot get any further than that.

Regards,

Peter