# Plot vector functions in different coordinate systems?

Posted 1 year ago
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 Hello to all:I teach physics at a community college in Arizona. Currently I am working on documents to assist students in visualization of Electrostatic and Magnetic fields. Almost all require either cylindrical or spherical coordinates. My question is: Given a field expressed in cylindrical coordinates, how do you generate a vector plot of the field in that coordinate system? Please note, that I have already found a method to convert the field from cylindrical to cartesian coordinates, and the VectorPlot function works just fine once I convert it, but I would like some options so that I do not need to convert the field but rather just plot it directly. This would also be helpful in the event that I want to visualize fields in other orthogonal coordinate systems e.g. toroidal coordinates.Thank you all for your consideration and responses.Chris Ubing Sierra Vista, Az
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Posted 10 months ago
 Seems not to be available directly by the usage of options to VectorPlot[]. But if e.g. there are the tangential vectors to a centered circle to be plotted VectorPlot[{-y, x}/Norm[{x, y}], {x, -3, 3}, {y, -3, 3}] this is in cylindrical co-ordinates {0, 1} or with other words AngleVector[ $\phi$] or with even other words VectorPlot[AngleVector[ArcTan[-y, x]], {x, -3, 
 You may use TransformedField to convert to Cartesian coordinates first, then use VectorPlot in the plane (or VectorPlot3D in 3-space) on the resulting field.
 Yes, VectorPlot[Evaluate[ TransformedField["Polar" -> "Cartesian", {0, 1}, {r, \[Theta]} -> {x, y}] ], {x, -3, 3}, {y, -3, 3}]