Easy gauss' law question that I wanna make sure I didn't make too easy

[schattenjaeger]

A sphere of radius a has its center at the origin, and has charge density p=Ar^2

another sphere of radius = 2a is concentric with the first. Find the flux SE*da through the larger sphere, where that's the surface integral of E dot da, like usual. It'd just be Qin/e where e is that constant, right? So I just have to do that volume integral that ends up having integrand Ar^2sin(theta) with r going from 0 to a, theta from 0 to pi, phi from 0 to 2pi?

And though it's not asked, if I DID want to find the electric field I'd note that da vector is r-hat*da and E only has the radial dependency, so Evector=Er*r-hat

so you end up with Er16pi*a^2=Qin/e solve for Er?

 

[Jhero]

Hi there,

Yes, you are correct in your approach for finding the flux through the larger sphere. The integral you have described is the correct one to use, and it will give you the total flux through the surface. As for finding the electric field, your method is also correct. Remember to include the constant of integration when solving for Er. Good luck with your calculations!