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Chapter 21 Electric Potential

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21 Electric Potential Slide 21-2

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Example Problem Answers for a positive test charge: a) 0; b) negative; c) positive; d) negative; e) zero; f) negative; g) zero (Instructor should state whether moving charge is positive, negative, or zero.) Is the change ∆U of the particle positive, negative, or zero as it moves from i to f? Slide 21-14

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**Electric Potential Energy**

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Electric Potential Slide 21-16

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**Conceptual Example Problem**

d) 1 = 2, 3 = 4 e) 1, 2, 3 Rank in order, from largest to smallest, the electric potentials at the numbered points. Slide 21-17

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**Charged Particle Moving Through a Potential Difference**

b) 3, 1 = 2 c) 3, 2, 1 d) 1 = 2, 3 = 4 e) 1, 2, 3 Slide 21-18

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Example Problem A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Slide 21-20

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A Topographic Map Slide 21-21

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**Graphical Representations of Electric Potential**

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Example Problem A proton is released from rest at point a. It then travels past point b. What is its speed at point b? Slide 21-23

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**Potential of a Parallel-Plate Capacitor**

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**The Potential Inside a Parallel-Plate Capacitor**

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Example Problem A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 105 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero). Slide 21-26

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**Electric Potential of a Point Charge**

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**Electric Potential: Charged Sphere**

Outside of a sphere of charge Q the potential has the same form as for a point charge Q: If the sphere has radius R and the potential at its surface is V0, then the potential a distance r from its center can also be written Slide 21-28

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**Example Problem For the situation shown in the figure, find**

The potential at points a and b.The potential difference between a and b. The potential energy of a proton at a and b. The speed at point b of a proton that was moving to the right at point a with a speed of 4.0 x 105 m/s. The speed at point a of a proton that was moving to the left at point b with a speed of 4.0 x 105 m/s. Slide 21-29

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**Example Problem A 2.0-mm-diameter plastic bead is charged to –1.0 nC.**

A proton is fired at the bead from far away with a speed of 1.0 x 106 m/s, and it collides head-on. What is the impact speed? An electron is fired at the bead from far away. It “reflects,” with a turning point 0.10 mm from the surface of the bead. What was the electron’s initial speed? Slide 21-30

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**Connecting Potential and Field**

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**Potential and Field for Three Important Cases**

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**Example Problem Source charges create the electric potential shown.**

What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude? Is the magnitude of the electric field at A greater than, equal to, or less than at point D? What is the approximate magnitude of the electric field at point C? What is the approximate direction of the electric field at point C? Slide 21-33

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**A Conductor in Electrostatic Equilibrium**

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Example Problem What is Q2? Slide 21-35

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**Capacitance and Capacitors**

The charge ±Q on each electrode is proportional to the potential difference ∆VC between the electrodes: Slide 21-36

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Charging a Capacitor Slide 21-37

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**The Capacitance of a Parallel-Plate Capacitor**

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**Dielectrics and Capacitors**

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Dielectric Constant With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ: Slide 21-40

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Summary Slide 21-41

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Summary Slide 21-42

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