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Chapter 21 Electric Potential Reading Quiz 1. What are the units of potential difference? Topics: • • • • • Electric potential energy Electric potential Conservation of energy Potential and field Capacitors and capacitance Sample question: Shown is the electric potential me easured on the surface of a patient. This potential is caused by electric trical signals originating in the beating heart. Why does the potential have this pattern, and what do these measurements tell us about the heart’s condition? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz Answer 2. New units of the electric field were introduced in this chapter. They are: A. V/C B. N/C C. V/m D. J/m2 E. Ω/m F. J/C 2. New units of the electric field were introduced in this chapter. They are: Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-2 C. V/m Slide 21-3 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-4 Reading Quiz Answer 3. The electric potential inside a parallel-plate parallel capacitor A. is constant. B. increases linearly from the negative to the positive plate. C. decreases linearly from the negative to the positive plate. D. decreases inversely with distance from the negative plate. E. decreases inversely with the square of the distance from the negative plate. 3. The electric potential inside a parallel-plate parallel capacitor Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-5 B. increases linearly from the negative to the positive plate. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz Answer 4. The electric field A. is always perpendicular to an equipotential surface. B. is always tangent to an equipotential surface. C. always bisects an equipotential surface. D. makes an angle to an equipotential surface that depends on the amount of charge. 4. The electric field A. is always perpendicular to an equipotential surface. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-7 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-6 Slide 21-8 Electric Potential Energy Potential Energy WAB = mghA − mghB = GPE A − GPE B Slide 21-9 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Potential Energy Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 10 Potential Energy WAB = EPE A − EPE B Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 11 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 12 The Electric Potential Difference The Electric Potential Difference DEFINITION OF ELECTRIC POTENTIAL The electric potential at a given point is the electric potential energy of a small test charge divided by the charge itself: WAB EPE A EPE B = − qo qo qo V= SI Unit of Electric Potential: The potential energy per unit charge is called the electric potential. joule/coulomb = volt (V) VB − VA = EPE B EPE A − WAB = − qo qo qo ∆V = Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 13 ∆(EPE ) − WAB = qo qo Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 14 Exercise Electric Potential Is the change ∆U of the particle positive, negative, or zero as it moves from i to f? U elec = qV; V = U elec / q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. EPE qo Slide 21-10 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11 A Topographic Map Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Graphical Representations of Electric Potential Slide 21-12 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 Slide 21-14 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-15 Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Example 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? A proton is released from rest att p point a. It then travels past point b. What is its speed at point b? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 The Potential Inside a Parallel-Plate Parallel Capacitor Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-17 Example A parallel-plate 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 plate capacitor is zero). V = Ex = Q ∆V x= C x ε0 A d Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-18 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-19 Electric Potential: Charged Sphere Electric Potential of a Point Charge Outside of a sphere of charge Q the th potential has the same form as for a point charge Q: V= 1 Q 4πε π 0 r 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 V=K 1 q q = r 4πε 0 r V= Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-20 R V0 r Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Example For the situation shown in the figure, find A 2.0-mm-diameter diameter plastic bead is charged to –1.0 nC. A. 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. head What is the impact speed? B. 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 21-21 A. The potential at points a and b.The potential difference between a and b. B. The potential energy of a proton at a and b. C. 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. D. 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. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-22 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-23 Connecting Potential and Field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Potential and Field for Three Important Cases Slide 21-24 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 A Conductor in Electrostatic Equilibrium Example Source charges create the electric potential shown. A. What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude? B. Is the magnitude of the electric field at A greater than, equal to, or less than at point D? C. What is the approximate magnitude of the electric field at point C? D. What is the approximate direction of the electric field at point C? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-26 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-27 Exercise Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ∆VC between the electrodes: Q = C∆VC What is Q2? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-28 Slide 21-29 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Capacitance of a Parallel-Plate Parallel Capacitor Charging a Capacitor C= Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-30 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. ε0 A d Slide 21-31 Dielectrics and Capacitors 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: C= Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-32 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-30 κε 0 A d Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-33