- #1

- 51

- 1

## Homework Statement

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.

## Homework Equations

Eq. (1): E⋅A=q

_{enc}/ε

Eq. (2): q

_{enc}=q⋅(r/R)

^{3}

In q

_{enc}, 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, q

_{enc}would be -30 μC. However, if I use Eq. (2), I get that q

_{enc}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 q

_{enc}be -30 μC, I get the following answer:

E= -6.7E6 N/C

If I'd used Eq. (2) to find q

_{enc}, 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!