Goal: Hone the concept of electrostatic potential
Source: 283-420 Change of PE

A uniform volume distribution of
charge has radius R and total charge Q. A point charge -q is released
from rest at point b, which is a distance 3R from the center of the
distribution. When the point charge reaches a, which of the following is
true regarding the potential energy, U?
- Ua = -Ub
- Ua = -2Ub/3
- Ua = -3Ub/2
- Ua = -9Ub/4
- Ua = Ub
- Ua = 2Ub/3
- Ua = 3Ub/2
- Ua = 9Ub/4
- None of the above
- Cannot be determined
Commentary:
Answer
(7) Many students use an inverse square dependence appropriate
for fields. Others will take the field at b and multiply by the
displacement. Still others will assert that the potential doubles
because they are using the distance to the surface of the sphere.