ELECTRIC POTENTIAL

1. ELECTRIC POTENTIAL September 19, 2008

2. Quizzicle

3. 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.

4. Electric Potential • We will be dealing with • Work • Energy & Conservation • Work must be done to move a charge in an electric field. • Let’s do a demo ….

5. I need some help. Push vs Pull Mrs. FIELDS vs Mr. External

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. 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.

8. Clearly • Both are doing work. • BOTH are applying a force through a distance. • BOTH get tired!

9. Each does the negative amount of work than the other does. WHY ?

10. 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.

11. 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.

12. And also remember: The net work done by a conservative (field) force on a particle moving around a closed path is ZERO!

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

14. The gravitational case: 

15. Someone else’s path 

16. IMPORTANT • 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!

17. 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 energy of the charge. • It is also the NEGATIVE of the work done BY THE FIELD in moving the charge from the same points.

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

19. Electric Potential Energy • When an electrostatic force acts between two or more charged particles, we can assign an ELECTRIC POTENTIAL ENERGY U to the system. • The change in potential energy of a charge is the amount of work that is done by an external force in moving the charge from its initial position to its new position. • It is the negative of the work done by the FIELD in moving the particle from the initial to the final position.

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. 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

24. UNITS OF POTENTIAL

25. Let’s move a charge from one point to another via an external force. • The external force does work on the particle. • The ELECTRIC FIELD also does work on the particle. • We move the particle from point i to point f. • The change in kinetic energy is equal to the work done by the applied forces. Assume this is zero for now.

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

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

28. One Step More

29. Consider Two Plates OOPS …

31. Look at the path issue

32. 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?

33. An ion accelerated through a potential difference of 115 V experiences an increase in kinetic energy of 7.37 × 10–17 J. Calculate the charge on the ion.

34. 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!

35. 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.

36. Example: A Set of Equipotenital Surfaces

37. Back To Yesteryear

38. Field Lines and Equipotentials Electric Field Equipotential Surface

39. Components Enormal Electric Field Dx Eparallel Work to move a charge a distance Dx along the equipotential surface Is Q x Eparallel X Dx Equipotential Surface

40. BUT • This an EQUIPOTENTIAL Surface • No work is needed since DV=0 for such a surface. • Consequently Eparallel=0 • E must be perpendicular to the equipotential surface

41. Therefore E E E V=constant

42. Field Lines are Perpendicular to the Equipotential Lines

43. Equipotential

44. ds V+dV V Consider Two EquipotentialSurfaces – Close together Work to move a charge q from a to b: b a E Note the (-) sign!

45. Where

46. Over a certain region of space, the electric potential is V = 5x – 3x2y +2yz2. Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of the field at the point P that has coordinates (1, 0, –2) m?

47. Typical Situation

48. Keep in Mind • Force and Displacement are VECTORS! • Potential is a SCALAR.

49. UNITS • 1 VOLT = 1 Joule/Coulomb • For the electric field, the units of N/C can be converted to: • 1 (N/C) = 1 (N/C) x 1(V/(J/C)) x 1J/(1 NM) • Or 1 N/C = 1 V/m • So an acceptable unit for the electric field is now Volts/meter. N/C is still correct as well.

50. In Atomic Physics • It is sometimes useful to define an energy in eV or electron volts. • One eV is the additional energy that an proton charge would get if it were accelerated through a potential difference of one volt. • 1 eV = e x 1V = (1.6 x 10-19C) x 1(J/C) = 1.6 x 10-19 Joules. • Nothing mysterious.