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Maxwell equations: Cartesian to Cylindrical coordinates

Posted 10 years ago

Hi, I am trying to express the following wave equation, which is expressed in Cartesian coordinates in Cylindrical coordinates:

\!\(\*SubsuperscriptBox[\(\[Del]\), \({x, y, z}\), \(2\)]\(Ez[x, y, z]\)\) + n^2 \[Omega] k0^2 Ez[x, y, z]

When I used FieldTransformed[], I get a result in unexpected format. Is there a simplified way to get the following, well known, wave equations expressed in Cylindrical coordinates starting from the Cartesian ones:

D[Ez[\[Rho], \[Phi], z], {\[Rho], 2}] + 
 1/\[Rho] D[Ez[\[Rho], \[Phi], z], \[Rho]] + 
 1/\[Rho]^2 D[Ez[\[Rho], \[Phi], z], {\[Phi], 2}] + 
 D[Ez[\[Rho], \[Phi], z], {z, 2}] + n^2 k0^2 Ez[\[Rho], \[Phi], z]

Thanks

POSTED BY: Saf Al
2 Replies

Try

Laplacian[Ez[\[Rho], \[Phi], z], 
{\[Rho], \[Phi], z},  "Cylindrical"] + n^2 \[Omega] k0^2 Ez[\[Rho], \[Phi], z] // Expand
POSTED BY: David Reiss
Posted 10 years ago

Indeed! The solution is simple and correct. Thanks.

POSTED BY: Saf Al
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