1. Previous Lecture Introduced Electrostatic Potential Energy (U el ) Electric Potential (V) Learned how to compute V for point charge charged sphere

2. Introduced the concept of electric field E to deal with forces Introduced electric potential V to deal with work and energy Electric potential: electric potential energy per unit charge Potential Energy Potential energy is associated with pairs of interacting objects A single particle has no electric potential energy

3. Potential Difference with Varying Field In general, integration path may be complex

4. Sign of the Potential Difference The potential difference  V can be positive or negative. The sign determines whether a particular charged particle will gain or lose energy in moving from one place to another. If q  V < 0 – then potential energy decreases and K increases If q  V > 0 – then potential energy increases and K decreases If there are no external forces acting on the system:

5. Example An electron traveling to the right enters capacitor through a small hole at A. Electric field strength is 2x10 3 N/C. What is the change in the electron’s potential energy in traveling from A to B? What is its change in kinetic energy?  AB)= 4mm = (1.6x10 -19 C)(2x10 3 N/C)(0.004m) =1.3x10 -18 J  K  U electric = -1.3x10 -18 J x

6. Example 30 0

7. Question 1 V 1 < V 2 A proton is free to move from right to left in the diagram shown. There are no other forces acting on the proton. As the proton moves from right to left, its potential energy: A)Is constant during the motion B)Decreases C)Increases D)Not enough information

8. If freed, a positive charge will move to the area with a lower potential: V f – V i < 0 (no external forces) V 1 < V 2 Moving in the direction of E means that potential is decreasing Sign of the Potential Difference

9. Question 2 V 1 < V 2 A system consists of a proton inside of a capacitor. The proton moves from left to right as shown at a constant speed due to the action of an external agent. Which of the following statements are true? A)The proton’s potential energy is unchanged and the external agent does no work on the system. B)The proton’s potential energy decreases and the external agent does work W > 0 on the system. C)The proton’s potential energy decreases and the external agent does work W < 0 on the system. D)The proton’s potential energy increases and the external agent does work W < 0 on the system. E)The proton’s potential energy increases and the external agent does work W > 0 on the system.

10. In most cases we are interested in  V, not the absolute values of V Shifting the Zero Potential

11. Potential Difference in a Nonuniform Field C x From A to C:  V 1 = -E 1x (x C -x A ); From C to B:  V 2 = -E 2x (x B -x C ); So, A to B:  V =  V 1 +  V 2 = -E 1x (x C -x A ) - E 2x (x B -x C )

12. i f Path independence principle:  V between two points does not depend on integration path Potential Difference: Path Independence

13. Need to find  V AC =V C - V A 1. Straight path A  C Example: Two Different Paths in Capacitor

14. Need to find  V AC =V C -V A 1. Straight path A  C 2. Path A  B  C Example: Two Different Paths in Capacitor

15. 1. Along straight radial path: riri rfrf +q+q Example: Different Paths near Point Charge

16. 2. Special case iA: AB: BC: Cf:Cf: Example: Different Paths near Point Charge +

17. 3. Arbitrary path + Example: Different Paths near Point Charge

18. Potential difference due to a stationary point charge is independent of the path Potential difference along a closed loop is zero Round Trip Potential Difference + A vector field is a conservative field if we can find a potential (scalar function) so that the vector field is the gradient of the potential.

19. Is the following “curly” pattern of electric field possible? dl Predicting Possible Field Configuration is always parallel to This “curly” pattern of electric field is impossible to produce by arranging any number of stationary point charges!

20. E d =3 mm +Q -Q  V = 6 Volt +3 V-3 V Charges are on surface Potential in Metal In static equilibriumA Capacitor with large plates and a small gap of 3 mm has a potential difference of 6 Volts from one plate to the other. Find E

21. d =3 mm +Q 1 -Q 1 1 mm Charges +Q 2 and –Q 2 What are the charges Q 1 and Q 2 ? Now we have 2 capacitors instead of one  V = 4 V There is no “conservation of potential”! Potential in Metal In static equilibrium Insert a 1 mm thick metal slab into the center of the capacitor. Metal slab polarizes and has charges +Q 2 and -Q 2 on its surfaces. Q 2 =Q 1 E inside metal is zero   V inside metal slab is zero!

22. http://www.alexandrosmaragos.com/2012/07/lightning-captured-at-7207-frames-per.html Physics of lightning Free path of e - in air at 1 atm, room T is about 1 micron (1*10 -6 m) Ionization potential of O 2 is 12.5eV, N 2 15 eV (1eV=1.6*10 -19 J is a kinetic energy which e - gains by going through  V=1 Volt) Approximate that about 10V is needed to ionize air. So, what will be E=  V/  x = 10/10 -6 = 10 7 V/m (close to E critical = 3*10 6 N/C we used in Lecture 7)

23. What is the change in electric potential energy associated with moving an electron from 1Å to 2Å from a proton? If an electron moves through a potential difference of 1 V there is a change in electric potential energy of 1 eV. 1 eV = e. (1 V) = (1.6. 10 -19 C)(1 V) = 1.6  10 -19 J Electron-Volt (eV) – Unit of Energy

24. Un importable from Feb 12 #8133A715,6 #8A55A27D,6 #95A4C6F7,6 #95AE9FA4,6