- #1

- 5

- 0

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

*i*bz]

the laplacian \/^2*Eo = ?

Eo is a vector

\/ is laplacian symbol

any help would be appreciated.

Thanks in advance.

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- Thread starter korps
- Start date

- #1

- 5

- 0

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

the laplacian \/^2*Eo = ?

Eo is a vector

\/ is laplacian symbol

any help would be appreciated.

Thanks in advance.

- #2

quasar987

Science Advisor

Homework Helper

Gold Member

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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.

- #3

HallsofIvy

Science Advisor

Homework Helper

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No, that's in "cylindrical coordinates" which is perfectly fine- just use polar coordinates with z appended.

The Laplacian of Y in cylindrical coordinates is

[tex]\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}[/tex]

The Laplacian of Y in cylindrical coordinates is

[tex]\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}[/tex]

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