Volumes in Charge symmetry anf distribution problems

[Vismay]

Hi everyone,
I am self-studying Electricity and Magnetism. I have a good grasp in Calculus, but still I am confused on how to figure out volumes of arbitrary figures(rest is easy). I know it's a bit silly. I mean how do we know how to choose a figure (like in case of hemisphere, you imagine rings inside hemisphere), how do we figure out cross sectional area and finally how do we set up integral. I mean I learned volume integrals in all coordinate systems, but they were different, i.e. they were simply bounded by some arbitrary surfaces or planes. Figuring out volume and cross-sectional areas is very difficult for me to grasp in Physics. That is more difficult than vector calculus. How do know that this part is dr, dx or we should now consider this angle to be dθ. I mean i understand the procedure, but don't know how, what and when to apply it. Possibly, because I started with a book called "Electricity and Magnetism" by Purcell. It has very very difficult problems. It is available on google play for review.

Please advice on what I must do next to understand this geometric concept in physics

 

[mathman]

I am not sure what is it about the physics that's bothering you. Look at the problem as a math question.