1. © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Lecture PowerPoints Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton

2. Chapter 24 Electric Potential

3. Main Points of Chapter 24 Definition of electric potential Calculation of electric potential of various charge distributions Equipotential surfaces, conductors, and the relationship between electric potential and electric field How a conductor’s shape affects the electric field Examples

4. 24-1 Electric Potential Energy (24-5) The potential energy of a point charge can be found from the Coulomb force:

5. 24-2 Electric Potential (24-6) (24-7) For a point charge: Electric potential = electric potential energy per unit charge; no dependence on test charge

6. Electric potential difference is also work needed per unit charge to move test charge through electric field Therefore, electric potential can be found by integrating the field along the path taken: 24-2 Electric Potential (24-9)

7. 24-2 Electric Potential The Electric Potential of Charge Distributions For a set of point charges: For a continuous distribution of charge:

8. 24-2 Electric Potential Units of Electric Potential Definition of the volt (energy per unit charge): Units of electric field – can write volts/meter as well as newtons/coulomb (24-13) (24-14)

9. The Electron-Volt 24-2 Electric Potential An electron-volt is the energy an electron gains when it is accelerated though a potential difference of one volt. Electron-volts are useful in atomic, nuclear, and particle physics.

10. 24-3 Equipotentials An equipotential surface connects points that are all at the same potential. The electric field is everywhere perpendicular to the equipotential surface. The surface of a conductor is an equipotential.

11. 24-3 Equipotentials Electric equipotential surfaces are analogous to contour lines on a topographic map (lines of constant elevation)

12. 24-4 Determining Fields from Potentials (24-29) To find the potential from the field: integrate along the path To find the field from the potential: take directional derivatives (24-9)

13. 24-5 The Potentials of Charge Distributions If the electric field is known: For a continuous charge distribution: For many point charges: For one point charge: (24-9) (24-7) (24-11) (24-12)

14. 24-6 Potentials and Fields Near Conductors Surface of a conductor is an equipotential Electric field is perpendicular to surface

15. 24-6 Potentials and Fields Near Conductors The Role of Sharp Points on Conducting Surfaces (24-37) Surface is equipotential Therefore, sharper points mean stronger fields Field strength is inversely proportional to radius of curvature

16. 24-7 Electric Potentials in Technology Van de Graaff Accelerator Produces highly energetic charged particles

17. 24-7 Electric Potentials in Technology Field-Ion Microscope Images of individual atoms

18. 24-7 Electric Potentials in Technology Xerography Relatively cheap way to make copies of anything that will fit on the glass

19. 24-7 Electric Potentials in Technology Scanning Tunneling Microscope Can image individual atoms Can also move single atoms to make desired configuration

20. Summary of Chapter 24 (24-6) Electric potential: (24-29) Relationship of field and potential: (24-9) Electric field is perpendicular to equipotential surface Surface of a conductor is an equipotential; field stronger where strongly curved