Finding the curl in diffrent coordinates by transforming variables

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SUMMARY

The discussion focuses on transforming the curl equation from Cartesian coordinates to cylindrical coordinates. The user attempted to rewrite the Cartesian basis vectors in terms of cylindrical coordinates (r, θ, z) and apply the Cartesian curl formula, but encountered incorrect results. Key insights include the necessity of recognizing that basis vectors differ in length and orientation between coordinate systems, which affects the transformation process. The user is encouraged to share their specific calculations for targeted feedback.

PREREQUISITES
  • Understanding of vector calculus, specifically curl operations.
  • Familiarity with coordinate transformations between Cartesian and cylindrical systems.
  • Knowledge of basis vectors and their properties in different coordinate systems.
  • Experience with partial differentiation in multivariable calculus.
NEXT STEPS
  • Study the derivation of curl in cylindrical coordinates using its definition.
  • Learn about the properties of basis vectors in different coordinate systems.
  • Explore examples of coordinate transformations in vector calculus.
  • Review the implications of vector field orientation on curl calculations.
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Students and professionals in mathematics, physics, and engineering who are working with vector calculus and coordinate transformations, particularly those dealing with fluid dynamics or electromagnetism.

sentinel
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we have a well known and simple equation for curl in cartesian coo. now we want it in let's say cylindrical coordinates.
question is...can we transform every thing to cylinderical and then use the formula for cartesian?I mean writing basis vectors of cartesian in terms of r and theta and z and basis vectors of cylindrical , and then write the x y z components of the vector(which we want its curl) in terms of its r and theta and z (cylindrical) components and then write the partial differentiations of cartesian in terms of cylindrical r and theta and then write the equation in cartesian>>transform everything to cylindrical>>get the desired formula!
I did this but it gave me wrong answer.WHY??!
I can and did derive the curl in different coordinates by using their definition but using the way I said above it should work...why not?
 
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Hey sentinel and welcome to the forums.

You should note that the basis vectors for the cartesian system are not going to necessarily be the same (length, orientation, etc) in the new system.

Without speculating, you should post what you did here so you can get some specific feedback and suggestions.
 

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