How Do You Calculate Field Point Vectors in Different Coordinate Systems?

[laura_kay]

I've been wanting to learn physics for a while, and bought an intro book and read through it. Now I want to move onto some higher level physics and am having some problem with the math. My book glosses over how to write out field point vectors, and I don't really understand it in various systems. In cartesian I think it's r-r', but I don't get it at all in cylindrical or spherical. Any help?

 

[arildno]

You really should buy a book on vector calculus as well. And work on it.

 

[Thetes]

In vector calculus, dimensions are broken up into independent components. But a vector has "length" and "direction", so it's not just a point in space. It has an associated length in whatever dimension the space you are looking at (for a cube then 3 dimension). Now, all these ideas become even more complicated when you start considering why space should be Cartesian at all (then you enter the world of Riemann and Einstein).

For a cylinder, you are locating points with a circle & height. The circle is composed of a radius & angle. So you can picture a cylinder being constructed at the origin of a Cartesian 3 space, with whatever parameters you want to set to describe the point. The sphere is very similar. Unfortunately, these descriptions are all still Cartesian space. So, as Gauss would point out, we can look at space with any unique identification that we want.