# Plot vector functions in different coordinate systems?

GROUPS:
 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
 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}]