A charge of -30 μC is distributed uniformly throughout a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.
Eq. (1): E⋅A=qenc/ε
Eq. (2): qenc=q⋅(r/R)3
In qenc, r is the radius of my Gaussian surface and R is the radius of the actual sphere, 10.0 cm.
The Attempt at a Solution
(a) E= -5.8E8 N/C
(b) E= -1.35E7 N/C
(c) This is where I'm a bit stuck. If I let the radius of my Gaussian surface be 20.0 cm, then all of the actual sphere will be enclosed in my surface. Therefore, qenc would be -30 μC. However, if I use Eq. (2), I get that qenc is -2.4E-6 C which wouldn't really make any sense. Why would there be more charge than what's given? Using what I feel is the more rational option (i.e. letting qenc be -30 μC, I get the following answer:
E= -6.7E6 N/C
If I'd used Eq. (2) to find qenc, I would've gotten E= -5.4E7 N/C. This doesn't make any sense to me, since E is proportional to the inverse radius squared.
I have no way to see if this problem is correct, as it comes from a textbook that only shows answers to odd problems and this is an even problem. Thank for any help in advance!