# Laplacian Help

I need to know the steps involved in solving this laplacian.

Ex(r,z) = Eo*e^[-(r/ro)^2]*e^[-ibz]

the laplacian \/^2*Eo = ?
Eo is a vector
\/ is laplacian symbol

any help would be appreciated.

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quasar987
Homework Helper
Gold Member
you probably meant \/^2*Ex, not \/^2*Eo.

Well, the problem is that there are polar and cartesian coordinates mixed up in the expression of Ex. So either transform r in cartesian and use the cartesian laplacian or transform z in polar and use the polar laplacian.

HallsofIvy
$$\frac{\partial^2 Y}{\partial r^2}+ \frac{1}{r}\frac{\partial Y}{\partial r}+ \frac{1}{r^2}\frac{\partial^2 Y}{\partial \theta^2}+ \frac{\partial^2 Y}{\partial z^2}$$