I'm trying to evaluate a line integral, Integration of Vector A dot dL
The vector A was given to be a function of r, theta and fi in spherical polar coordinates.
The question states that an arbitrary closed loop C is the circle parametrised by fi at some arbitrary values of (r, theta).
I would like to ask the following questions:
(i) How do I rewrite dl, the line element, in terms of spherical polar co-ordinates? What does it mean by the closed curve C is the circle parametrised by fi at some arbitrary values of (r, theta). How does it change my dl if C wasn't a circle?
(ii) What are the limits of the line integral?