1. Physics 212 Lecture 6, Slide 1 Physics 212 Lecture 6 Today's Concept: Electric Potential Defined in terms of Path Integral of Electric Field

2. Main Point 1 First, the electric potential is a scalar function defined at all points in space that can be used to determine all electrostatic effects produced by a specified charge distribution. The change in electric potential between any two points is defined to be the energy required to move a unit positive charge between the two points. In particular, the change in potential between points a and b can be calculated as minus the integral of E dot dl along any path from a to b. The electric potential at a given point is then defined to be the change in potential between that point and an arbitrary point chosen to be the zero of electric potential. Physics 212 Lecture 6, Slide 2

3. Main Point 2 Second, an equipotential is defined to be the locus of all points having the same potential. These equipotentials are always perpendicular to electric field and their spacing indicates the strength of the electric field, how fast the potential is changing. Physics 212 Lecture 6, Slide 3

4. Main Point 3 Third, the electric field (a vector) can be obtained from the electric potential (a scalar) at any point in space by applying the gradient function, i.e., E = -gradient(V). The electric field is simply a measure of how fast the electric potential is changing. Physics 212 Lecture 6, Slide 4

5. Physics 212 Lecture 6, Slide 5 40

6. Physics 212 Lecture 6, Slide 6 Checkpoint 1a 08

7. Physics 212 Lecture 6, Slide 7 Checkpoint 1b 08 A B C D

8. Physics 212 Lecture 6, Slide 8 40

9. Physics 212 Lecture 6, Slide 9

10. Physics 212 Lecture 6, Slide 10 Checkpoint 2 08 A B C D

11. Physics 212 Lecture 6, Slide 11 Checkpoint 3a 08 A B C D

12. Physics 212 Lecture 6, Slide 12 Checkpoint 3b 08 A B C D A B C D

13. Physics 212 Lecture 6, Slide 13 Checkpoint 3c 08 A B C D A B C D

14. Physics 212 Lecture 6, Slide 14

15. Physics 212 Lecture 6, Slide 15 E from V If we can get the potential by integrating the electric field: 40 We should be able to get the electric field by differentiating the potential?? In Cartesian coordinates:

16. Physics 212 Lecture 6, Slide 16Equipotentials Equipotentials are the locus of points having the same potential 40 Equipotentials produced by a point charge Equipotentials are ALWAYS perpendicular to the electric field lines The SPACING of the equipotentials indicates The STRENGTH of the electric field

17. Physics 212 Lecture 6, Slide 17

18. Physics 212 Lecture 6, Slide 18

19. Physics 212 Lecture 6, Slide 19 Example Problem Point charge q at center of concentric conducting spherical shells of radii a 1, a 2, a 3, and a 4. The inner shell is uncharged, but the outer shell carries charge Q. What is V as a function of r? q metal Q a1a1 a2a2 a3a3 a4a4 Conceptual Analysis: Strategic Analysis: cross-section

20. Physics 212 Lecture 6, Slide 20 Example Problem: Quantitative Analysis q metal Q a1a1 a2a2 a3a3 a4a4 cross-section

21. Physics 212 Lecture 6, Slide 21