Understanding Length and Area Elements for Electromagnetic Laws

[tblount2]

I'm having a difficult time figuring out how to find length and area elements for Gauss's, Ampere's, and Biot-Savart Laws! Can someone please help explain! This applies to symmetrical, non-symmetrical, and infinite objects! I'm not asking what is the area of a sphere but, say with an infinite object, you use a small portion maybe called ds, well how do you figure how what your value of ds will be? And please don't give an example using a simple figure! That won't help me! I've noticed that if I understand the most difficult then I'm good to go for everything! Thanks :)

 

[met4t]

ds is an infinitesimal distance which u can chose in cartesian coordinates, cylindrical or spherical coordinates. U want to chose ds along the line which contains the flux or the current, ...

 

[HallsofIvy]

You don't "figure out your value of ds". A differential has no value in terms of numbers. You integrate with respect to s.