A2L Item 129

• Description: Identify the correct relationship for potentials when the distance between charges changes.
• Goal: Hone the concept of electrostatic potential
• Source: 283-420 Change of PE
• Keywords: Distributed Charges, Electromagnetism, Potential Energy

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The question for students:

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?

1. U_a = -U_b
2. U_a = -2U_b/3
3. U_a = -3U_b/2
4. U_a = -9U_b/4
5. U_a = U_b
6. U_a = 2U_b/3
7. U_a = 3U_b/2
8. U_a = 9U_b/4
9. None of the above
10. Cannot be determined

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Commentary for teachers:

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.

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