# Maxwell equations: Cartesian to Cylindrical coordinates

Posted 9 years ago
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 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
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Posted 9 years ago
 Try Laplacian[Ez[\[Rho], \[Phi], z], {\[Rho], \[Phi], z}, "Cylindrical"] + n^2 \[Omega] k0^2 Ez[\[Rho], \[Phi], z] // Expand 
Posted 9 years ago
 Indeed! The solution is simple and correct. Thanks.