1. The problem statement, all variables and given/known data The problem deals with a charged (Q) rotating sphere around its axis (Ω_0) z^^ (z hat) of radius a. I'm asked to find the total angular momentum of the EM fields. 2. The attempt at a solution There is a solution posted to this question and I was just wondering why my calculation aren't right. Please give it a look: http://docdro.id/WcBxAKH [Broken] I understand the calculation itself and how they've gotten to their final answer and all that but what I'm unable to get yet is why write theta in Cartesian coordinates in the first place? Why can't I keep it as the unit vector theta? Am I not allowed to take it (unit vector theta) out the integral and then calculate? Or in general, when am I allowed to take unit vectors out the integrals when calculating something and when am I not? Thanks in advance.