Problem 9. Mr) 2' Suppose you have a solid sphere with a radius R and a spherically symmetric charge density % = p(r). Use Gauss's Law to find the electrostatic field(s) at all , points in space for: y a) A uniform charge density p('r) = p0 for r g R. X b) A non-uniform charge density p(r) = 91% kthot r2 I Note that this problem requires you to do an integral to evaluate the total charge inside a Gaussian surface. I'll help you set it up. The volume of a differentially thin spherical shell is its area A = 4m~'2 times its thickness dr': In both cases, show that the field outside of the sphere is E = d]? = 47rr'2dr" The (differential) charge in this shell is therefore: 0362 = p('r") de(r') = 47rr'2dr' where you have to substitute in the p(r') given above for at least the second case. If you integrate this from r' = U > r you will have Q('r), the total charge inside the radius 7'. Note that I use r' instead of r as the variable to integrate over so you can make 1" (itself a variable for the GLE part of the solution) a limit of integration remember how that works