1. Work done by a force “on” a particle that travels from A to B
Energy refresher course:
Work done by a force “on” a particle that travels from A to B
Constant force only!

2. The work-energy theorem
Work done by all forces acting!
Change in particle’s kinetic energy

3. Energy refresher course:

4. Energy refresher course:
For F a conservative force!

5. Energy refresher course:
For F a conservative force!

6. Energy refresher course:
For F a conservative force!

7. So, what kind of Work can be done by ?
Can we define a PE function associated with ?
(i.e. is the Coulomb force conservative?)

8. Electric Potential

9. Electric Potential A

10. Electric Potential A

11. Electric Potential A

12. Electric Potential A B
Path 1

13. Electric Potential A

14. Test charge +q
What’s the work done on +q by in going from A to B?

15. A B

16. Electric Potential A

17. Electric Potential A

18. Electric Potential A B
Path 2

19. Electric Potential A B

20. The Coulomb force is conservative! SO:
It turns out:
when a charge Q is moved from (any) point A to B,
the work done on it by ‘any’ electric field
is independent on the route taken from A to B
The Coulomb force is conservative!
SO:
we can define a potential energy function!

21. Electric potential: V (not quite an energy)
Units:
Units:

22. Electric potential: V (not quite an energy)
Difference in ‘electric
potential’ between
point B and A.
work done by the electric
field on a charge q in moving
from A→B.

23. Volts! Unit of electric potential
MKS unit of electric
potential
Electron-volts! Unit of energy
For work involving atomic-scale interactions e is much more convenient
as a measure of charge, so alternate energy units:

24. Work-energy example: A IF the electric force is the only force acting!B
(next)

25. Work-energy example: A B
(next)

26. Work-energy example: A B
(figure it)

27. Work-energy example:
(what if we had a negative charge at A?) A B

28. The moral: Positive charges want to go to places of lower V
Negative charges want to go to places of higher V

29. These change from place to place …
TOTAL Energy
Potential Energy
Kinetic Energy
… but this is a constant!
These change from place to place …

30. B ? A
Next …

31. 1. Figure U from data at A B ? A

32. 2. Now use U to figure v at B B A

33. Energy [J]
position x

34. Energy [J]
position x

35. Energy [J] A
position x

36. Energy [J] B A
position x

37. Energy [J] A B
position x

38. How do we figure the electric potential?
If we know the electric field, then we can calculate the work done between any two points, and use one of those points as a fixed reference
Example …

39. Constant
0 cm x
1 cm

40. test charge +q
0 cm x
1 cm

41. test charge +q
0 cm x
1 cm

42. 0 cm x
1 cm

43. Set arbitrarily
x = d
0 cm
1 cm

44. + 100 V
+ 10 V
position x
0 cm
1 cm

45. put in q = +10 mC at rest + 1.0 J + 0.1 J 0 cm 1 cm position x High V
Low V
10V

46. put in q = +10 mC at rest + 1.0 J + 0.1 J 0 cm 1 cm position x High V
Low V
10V

47. put in q = -20 mC at rest - 0.2 J - 2.0 J 0 cm 1 cm position x High V
Low V
10V

48. put in q = -20 mC at rest - 0.2 J - 2.0 J 0 cm 1 cm position x High V
Low V
10V

49. The moral: Positive charges want to go to places of lower V
Negative charges want to go to places of higher V