Vectors in different coordinate systems

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1. Oct 24, 2014

how do i write vectors in polar coordinate? And what will the azimuth coordinate represent?

I was trying to figure out the vector connecting a ring to its center using polar coordinates, so that i would perform an integration over d(phi) (finding the electric field due to a semicircle at the origin). I wrote the vector as (-rho, phi,0) but then i ran into trouble with the units since the units of phi are radians. I worked this out in cartesian pretty easily but i am eager to know how this will work in polar, since polar here seems to me more natural.

2. Oct 24, 2014

Staff: Mentor

Welcome to PF!

I think you need to include the radius as one component. In your integration you need the Jacobian too
as in r dr dtheta which provides the missing units of measure.

Here's some info on polar coordinates and circles:

http://en.wikipedia.org/wiki/Polar_coordinate_system#circle

3. Oct 24, 2014

I know the jacobian, and infact already found it in this case, but the issue is not here. Here the vector is included in the integration, but the phi component has units radians, while the rho has meters. The idea here is that maybe my idea about vectors in cylindrical / polar coordinates is wrong. This is so since the length of a vector can not be (rho + phi)^1/2 since the rho and phi have different units.

4. Oct 24, 2014

Rho^2 +phi^2 (first post sorry)

5. Oct 24, 2014

6. Oct 24, 2014

Here is the problem.. I am stuck at finding the vector that goes from the ring to the origin. And assuming i know that vector, which phi should i use to obtain the value of the electric field at the origin? I mean phi changes with position. I realise there is an easier way, but i want to know this way as well. (Sorry for multiple posts, this is my first time using a forum, soi am not sure i get the hang of it)

7. Oct 24, 2014

Staff: Mentor

As I look at the wolfram examples like arc length, they don't treat the vector in a component fashion but as a vector.

http://mathworld.wolfram.com/PolarCoordinates.html

And that may be why you hung up here, you're trying to work with it in its native form.

I think they would define your vector as being normal to the arc ie the second derivative of the arc line.

Last edited: Oct 24, 2014