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Let's say we have a vector field that looks similar to this. Assume that the above image is of the x-y plane.

The vector arrows circulate a central axis, you can think of them as tangents to circles.

The field does not depend on the height z.

The lengths of the arrows is a function of their radial distance from the center/axis,

*.*

**f(r)**How do we write this vector field in terms of Cylindrical coordinates?

##A_\rho \hat{\boldsymbol \rho} + A_\varphi \hat{\boldsymbol \varphi} + A_z \hat{\mathbf z}##

How does one find ##A_\rho , A_\varphi## and ##A_z ## ?