- #1
Stendhal
- 24
- 1
Homework Statement
Is there a more intuitive way of thinking or calculating the transformation between coordinates of a field or any given vector?
The E&M book I'm using right now likes to use the vector field
## \vec F\ = \frac {\vec x} {r^3} ##
where r is the magnitude of ## \vec x ##In Cartesian coordinates, this looks like
## \frac {x \hat x + y \hat y + z \hat z} {\sqrt {x^2 + y^2 +z^2}^3} ##
In problems such as finding the flux through a sphere, it's difficult to use cartesian coordinates as it's very algrebra intensive, but I find it hard to convert between different coordinate systems. It also seems really unnecessary to simply look up the values of x,y,z and their respective ## \hat x ## directions for the components. Is there a better way to go about thinking and converting fields?