Del Operator for Cylindrical Coordinate

[Harmony]

http://img208.imageshack.us/img208/5153/12802868.png

Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

 

[bartek2009]

You could read about general curvilinear coordinates and that should answer your question (plus it will also explain the factors in other expressions from different coordinate systems like e.g. spherical polar coordinates). Basically the unit vectors change with position in cylindrical coordinates and that is why the factor appears.

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[tiny-tim]

Hi Harmony!

(have a del: ∇ and a theta: θ and a curly d: ∂ )

Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

(∇).e_θ has to be the rate of increase per distance in the e_θ direction …

but ∂/∂θ is the rate of increase per angle …

and distance (in the e_θ direction) is r times angle.

 

[befangler]

How does the 1/r term arises?

I had the same question and found this nice derivation in "Engineering Electromagnetics" by Nathan Ida available for preview on Google Books. Link below:

http://books.google.com/books?id=2C...nepage&q=del cartesian to cylindrical&f=false

The derivation starts on page 80 which is available for viewing without purchase.
Hope this helps.

 

[befangler]

Also, in case the link I provided in my previous post becomes unavailable, PF members arildno and HallsOfIvy walk through the same derivation in another thread here on Physics Forum.

Check it out under Physics Forums>Mathematics>General Math -> Thread = "Del operator with coordinate transformations"