A non-conducting sphere of radius R has volume charge density ρ = B/r. for r<R and ρ = - for r>R. B is a constant.
a) Calculate E-field for r>R.
b) Calculate E-field for r<R.
c) Calculate potential for r>R.
d) Calculate potential for r=R.
e) Calculate potential for r<R
The Attempt at a Solution
Well first of all I was a bit confused on the whole ρ = 0 when r>R, but apparently that just means that all of the charge is contained within the sphere.
So since it is a nonuniform charge, I first found the charge of the sphere. ∫(0 to R)ρ4πr^2dr and got 2BπR^2.
I'm pretty confident about all my answers except for part e) For part a) I did E4πr^2=2BπR^2/ε and got E=BR^2/2r^2ε. Same thing for part b, but this time the radius cancels out so B/2ε
So for part c I took the negative integral of the e-field outside of R. V=-∫(BR^2/2r^2ε)dr and ended up with BR^2/2rε. Same thing for part d, but the radius cancels out.
Now part e I did the same thing -∫B/2εdr and got -Br/2ε. I feel like it might be wrong since it's negative, and I don't really understand why the potential inside the sphere would be negative