Chapter 18 – Part I -Potential

1. Chapter 18 – Part I -Potential

2. Things to remember • Definition of WORK • W=F d cos(q) • Definition of Potential Energy • Work necessary to bring an object from some reference level to the final position. • For the diagram • PE=Mgh M

3. Quizzicle

4. Picture a Region ofspace Where there is an Electric Field • Imagine there is a particle of charge q at some location. • Imagine that the particle must be moved to another spot within the field. • Work must be done in order to accomplish this.

5. What (or who) must do this work? • An external agent (person) • The Field itself • Either of the above • Dr. Bindell

6. What we will do …. E • For the moment, assume the charge has MASS. (It may not.) • Assume the charge is initially stationary. • The charge is to be moved to the left. • The charge is to be moved at CONSTANT velocity. + charge Mrs. Fields Mr. External

7. During this process, who is pushing? E • Mr. External • Mrs. Fields • Dr. Bindell + charge Mrs. Fields Mr. External

8. When we start the process, the charge that is stationary must be brought up to speed. • This is work and must be accounted for. • This is work but we don’t have to worry about it. • Only Dr. Bindell worries about stupid stuff like this!

9. About the work that they do .. • Mrs. Fields does more work than Mr. External. • Mr. External does more work than Mrs. Fields. • Both do the same amount of work. • Each does the negative amount of work than the other does.

10. Start and Sop • ENERGY is required to bring the charge up to speed (if it has mass). • ENERGY is required to bring the particle back to rest (if it has mass). • The sum of these two is ZERO.

11. So, when we move a charge in an Electric Field .. • Move the charge at constant velocity so it is in mechanical equilibrium all the time. • Ignore the acceleration at the beginning because you have to do the same amount of negative work to stop it when you get there.

12. Summary-- • When an object is moved from one point to another in an Electric Field, • It takes energy (work) to move it. • This work can be done by an external force (you). • You can also think of this as the FIELD doing the negative of this amount of work on the particle.

13. And also remember: The net work done by a conservative (field) force on a particle moving around a closed path is ZERO! Huh? What does this mean??

14. A nice landscape Work done by external force = mgh How much work here by gravitational field? h  mg

15. The gravitational case: 

16. Someone else’s path 

17. IMPORTANT (For a conservative field) • The work necessary for an external agent to move a charge from an initial point to a final point is INDEPENDENT OF THE PATH CHOSEN!

18. The Electric Field • Is a conservative field. • No frictional losses, etc. • Is created by charges. • When one (external agent) moves a test charge from one point in a field to another, the external agent must do work. • This work is equal to the increase in potential energyof the charge. • It is also the NEGATIVEof the work done BY THE FIELD in moving the charge from the same points.

19. A few things to remember… • A conservative force is NOT a Republican. • An External Agent is NOT 007.

20. Definition – Potential Energy • PE or U is the work done by an external agent in moving a charge from a REFERENCE POSITION to a different position. • A Reference ZERO is placed at the most convenient position • Like the ground level in many gravitational potential energy problems.

21. Zero Level Example: E Work by External Agent Wexternal = Fd = qEd= U Work done by the Field is: Wfield= -qEd = -Wexternal d q F

22. A uniform electric field of magnitude 290 V/m is directed in the positive x direction. A +13.0 µC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm).(a) What is the change in the potential energy of the charge field system?[-0.000754] J

23. YOU Think about YOU being the external agent and you are therefore doing the work.

24. Parallel Sheets of Charge

25. Parallel Sheets of Charge II

26. Get to Work + + q’ q

28. IMPORTANT RESULT The potential energy U of a system consisting of two charges q and q’ separated by a distance r Is given by: This also applies to multiple charges.

29. What is the Potential Energy of q’? Unit is JOULES

30. AN IMPORTANT DEFINITION • Just as the ELECTRIC FIELD was defined as the FORCE per UNIT CHARGE: We define ELECTRICAL POTENTIAL as the POTENTIAL ENERGY PER UNIT CHARGE: VECTOR SCALAR

31. UNITS OF POTENTIAL

32. Furthermore… If we move a particle through a potential difference of DV, the work from an external “person” necessary to do this is qDV

33. Electric Field = 2 N/C  d= 100 meters 1 mC Example

34. One Step More

35. Consider Two Plates OOPS!

37. The difference in potential between the accelerating plates in the electron gun of a TV picture tube is about 25 000 V. If the distance between these plates is 1.50 cm, what is the magnitude of the uniform electric field in this region?

38. Important • We defined an absolute level of potential. • To do this, we needed to define a REFERENCE or ZERO level for potential. • For a uniform field, it didn’t matter where we placed the reference. • For POINT CHARGES, we will see shortly that we must place the level at infinity or the math gets very messy!

39. An Equipotential Surface is defined as a surface on which the potential is constant. It takes NO work to move a charged particle between two points at the same potential. The locus of all possible points that require NO WORK to move the charge to is actually a surface.

40. Example: A Set of Equipotenital Surfaces

41. Example

42. What is the Potential Energy of q’? Unit is JOULES Units are VOLTS

43. Imagine a 1 Coulomb charge at each point. How much work did it take to create this Charged triangle??