Understanding Electric Potential and Fields

1. ELECTRIC POTENTIAL September 13, 2006

2. Goings On For the Next Few Days • Quiz Today – Gauss/Electric Field • Today – Begin Chapter 25 – Potential • Monday - Potential • Wednesday – EXAMINATION #1 • Friday – More Potential

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 moves to another spot within the field. • Work must be done in order to accomplish this.

5. Electric Potential • We will be dealing with • Work • Energy • We do work if we try to move a charge in an electric field. • Does the FIELD do work? • Does the FIELD have a brain? Muscles?

6. Energy Methods • Often easier to apply than to solve directly Newton’s law equations. • Only works for conservative forces. • One has to be careful with SIGNS. • VERY CAREFUL!

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

8. THINK ABOUT THIS!!! • 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.

9. Move It! • 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.

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

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

12. The gravitational case: 

13. Someone else’s path 

14. 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!

15. 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.

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

17. 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.

18. Example: NOTATION U=PE HIGH U LOWER U E  q F A B d d Work done by FIELD is Fd Negative of the work done by the FIELD is -Fd Change in Potential Energy is –Fd. The charge sort-of “fell” to lower potential energy.

19. Another way to look at it: • Consider an external agent. • The external agent moves a charge from one point to the other. • The work done by the external agent in moving the charge between these points is the change in potential energy. • This is the negative of the work that the FIELD does!

20. Electrons have those *&#^ negative signs. • Electrons sometimes seem to be more difficult to deal with because of their negative charge. • They “seem” to go from low potential energy to high. • They DO! • They always fall AGAINST the field! • Strange little things. But if YOU were negative, you would be a little strange too!

21. 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

22. UNITS OF POTENTIAL

23. 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.

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

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

26. One Step More

27. Consider Two Plates OOPS …

29. Look at the path issue

30. 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?

31. 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.

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

33. 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.

34. Example: A Set of Equipotenital Surfaces

35. Back To Yesteryear

36. Field Lines and Equipotentials Electric Field Equipotential Surface

37. 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

38. 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

39. Therefore E E E V=constant

40. Field Lines are Perpendicular to the Equipotential Lines

41. Equipotential

42. 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!

43. Where

44. 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?

45. Typical Situation

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

47. 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.

48. 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.

49. Coulomb Stuff: A NEW REFERENCE: INFINITY Consider a unit charge (+) being brought from infinity to a distance r from a Charge q: x r q To move a unit test charge from infinity to the point at a distance r from the charge q, the external force must do an amount of work that we now can calculate.

50. Just Do It!