1. 4/22/16Oregon State University PH 213, Class #121 Summary of Electrostatics Field“payload”Effect E · q = F E = –dV/ds F = –dU E /ds V · q = U E

2. 4/22/16Oregon State University PH 213, Class #122 The Voltage Difference Created by a Set of Parallel Plates Since the E-field between two plates is a constant, it’s easy to find the work necessary to move a charge against that field (just like moving a mass against a constant local g) for a distance  d:  W  =  U E  =  qE  d  So the potential difference (also called the voltage difference) magnitude is  V  =  U E /q  =  E  d  But you are moving a displacement  d against the field to increase voltage:  V =  U E /q = –  E  d So in general (not just between plates):  E  = –dV/ds, where ds is an incremental distance moved along the direction of E.

3. A capacitor is essentially a pair of parallel, oppositely-charged conductive plates. The electric potential inside a capacitor… 1.is constant 2.increases linearly from the negative to the positive plate 3.decreases linearly from the negative to the positive plate 4.decreases inversely with distance from the negative plate 5.decreases inversely with the square of the distance from the negative plate 4/22/163Oregon State University PH 213, Class #12

4. The electric potential inside a capacitor 1.is constant 2.increases linearly from the negative to the positive plate 3.decreases linearly from the negative to the positive plate 4.decreases inversely with distance from the negative plate 5.decreases inversely with the square of the distance from the negative plate 4/22/164Oregon State University PH 213, Class #12

5. Rank in order, from largest to smallest, the potentials V a to V e at the points a to e. 1.V d = V e > V c > V a = V b 2.V b = V c = V e > V a = V d 3.V a = V b = V c = V d = V e 4.V a = V b > V c > V d = V e 5.V a = V b = V d = V e > V c 4/22/165Oregon State University PH 213, Class #12

6. Which electric potential graph describes this electric field? 4/22/166Oregon State University PH 213, Class #12

7. Which electric potential graph describes this electric field? 4/22/167Oregon State University PH 213, Class #12

8. 4/22/16Oregon State University PH 213, Class #128 Summary of Electrostatics Field“payload”Effect E · q = F E = –dV/ds F = –dU E /ds V · q = U E

9. 4/22/16Oregon State University PH 213, Class #129 The Strength of the Electric Potential Field (Voltage) Created by a Point Charge Q: It’s all well and good to look at simple, uniform electrical fields between parallel charged plates, but what about when the fields are not uniform—such as when point charges create them? What is the electric potential (voltage) at any point in space due to a nearby point charge, q? A: V = kq/r, where r is the distance from q to the point in question. This is a result of integrating Again, the sign of the charge again indicates how the potential changes in the space around it. Note where we have selected V = zero only at an infinite distance from q. (The analogy to gravity goes on.)

10. Rank in order, from largest to smallest, the potential energies U a to U d of these four pairs of charges. Each + symbol represents the same amount of charge. A. U a = U b > U c = U d B. U b = U d > U a = U c C. U a = U c > U b = U d D. U d > U c > U b > U a E. U d > U b = U c > U a 4/22/1610Oregon State University PH 213, Class #12

11. Rank in order, from largest to smallest, the potential energies U a to U d of these four pairs of charges. Each + symbol represents the same amount of charge. A. U a = U b > U c = U d B. U b = U d > U a = U c C. U a = U c > U b = U d D. U d > U c > U b > U a E. U d > U b = U c > U a 4/22/1611Oregon State University PH 213, Class #12

12. Rank in order, from largest to smallest, the electric potentials (“voltages”) of these four collections of charge [measured at the midpoint between them]. Each + symbol represents the same amount of charge. 4/22/1612Oregon State University PH 213, Class #12 [Voltage is a field—a description of a certain property—of a point in space, so we must specify that point.]