Question

A sphere of radius r =5cm and volume charge density ρ=14μC/m^3 spins at ω=200rad/s
. What is the magnetic field at the center of the sphere in Tesla?

Answer 1

You have a solid sphere. this requires a lot of integration. Here is an example of just a spherical radius, examine it, then adapt it for an inegration thru dr.

https://ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/exams/MIT8_07F12_quizsol2.pdf