1. (1) I have completed at least 50% of the reading and study- guide assignments associated with the lecture, as indicated on the course schedule. a) Trueb) False iClicker Quiz

2. Force is a vector. Differential path length is a vector. Work is a scalar quantity. Only the force component along the motion direction does work. Pulling a cart through deep sand (motion parallel to force). a b F app dsds

3. dsds 0   0 + Work done by F g : Work done by gravity

4. x m Change in gravitational potential energy = (  )work done by gravity

5. x Work done by gravity m

6. Gravitational potential Gravitational potential is not the same as potential energy. It ’ s the energy/mass that a test mass would possess if present. No test mass is needed for a gravitational potential to exist. One mass possesses a potential. Two masses interact to have potential energy.

7. ForcePotential Energy PotentialField

8. Electric potential Electric potential is not the same as potential energy. It ’ s the energy/charge that a test charge would possess if present. No test charge is needed for an electric potential to exist. One charge possesses a potential. Two charges interact to have potential energy.

9. ForcePotential Energy PotentialField

10. ForcePotential Energy PotentialField

11. Gradient: a three-dimensional derivative (three derivatives instead of one) A gradient always points in the direction of steepest ascent. An E-field always points in the direction of steepest descent.

12. Vector fields point downhill in potential (V). Forces point downhill in energy (U). E - F + F +V+V VV +U+U UU +U+U UU 100 V 0 V

13. e Static E-fields are conservative, which implies that the potential difference between two points is independent of the path travelled! 1 V 0 V E b a An electron (or protron) passing through a 1 Volt potential difference experiences a 1 electron-Volt (eV) change in potential energy.

14. e 1 V 0 V E A free charge passing through a potential difference will experience a change in kinetic energy opposite to its change in potential energy.

15. Quiz: Which movement requires us to do the most positive work? Consider moving a positive test between the following points on the equipotential surfaces shown. (1) A-B (2) B-C (3) C-D (4) D-E Quiz: Which movement involves no work? Quiz: Which movement lowers the potential energy the most? Which way does the field point?

16. ForcePotential Energy PotentialField Special case: point charge

17. Electric potential near point charges +  Which way will the field point? (a) +x (b)  x (c) +y (d)  y Which way will the force point? (a) +x (b)  x (c) +y (d)  y negative test charge

18. r R: ∞ → r Point-charge example: use E to obtain V.

19. Example of a potential gradient calculation

20. Point-charge example: use V to obtain E.

21. Potential from a conducting sphere with charge Q on the surface

22. Potential: positively-charged conducting shell, or an insulating shell with uniform surface charge density E V

23. V(1,1,1) = 10 VoltsFind V(1,0,1) y x z (1,1,1) (1,0,1)

24. V(0,0,0) = 0 Volts Find V(1,1,1) x z y

25. Infinite line charge E 0 0 Neither zero nor infinity are convenient zero-voltage references.

26. Field lines and equipotential surfaces for a few simple configurations: uniform, monopole, and dipole fields. Equipotential surfaces are pendicular to the field lines at every point, and densely spaced when the field lines are densely spaced. They are like elevation contours on a topographical map – it marks a region of constant voltage (height).

27. http://geology.isu.edu/geostac/ Field_Exercise/topomaps/ Quiz: Where is the electric potential greatest?

28. p

29. In electrostatic equilibrium, conducting objects are equi- potential bodies, and therefore have equipotential surfaces.

30. Despite a complicated surface charge density, the entire surface of the conducting sphere has the same potential.

31. Insulating ring of radius a and linear charge density a

32. Insulating annulus with uniform surface charge density , inner radius a and outer radius b

33. Potential from a conducting sphere with charge Q on the surface dQ

34. Point charge potential E V

35. Potential: positively-charged solid conducting sphere E V

36. Potential: positively-charged conducting shell, or an insulating shell with uniform surface charge density E V

37. Potential: positively-charged solid insulating sphere E V

38. Positive point charge within a thick neutral conducting shell E V

39. Negative point charge within a thick neutral conducting shell V E