1. Electric Potential
and Capacitance

2. Electric Potential Energy and Potential Difference
Relation between Electric Potential and Electric Field
Equipotential Lines
The Electron Volt, a Unit of Energy
Electric Potential Due to Point Charges
Potential Due to Electric Dipole; Dipole Moment

3. Capacitance
Dielectrics
Storage of Electric Energy
Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
The Electrocardiogram (ECG or EKG)

4. Electrostatic Potential Energy and Potential Difference
The electrostatic force is conservative – potential energy can be defined
Change in electric potential energy is negative of work done by electric force:

5. Electrostatic Potential Energy and Potential Difference
Electric potential is defined as potential energy per unit charge:
Unit of electric potential: the volt (V).
1 V = I J/C.

6. Electrostatic Potential Energy and Potential Difference
Only changes in potential can be measured, allowing free assignment of V = 0.

7. Electrostatic Potential Energy and Potential Difference
Analogy between gravitational and electrical potential energy:

8. Relation between Electric Potential and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by distance:

9. Relation between Electric Potential and Electric Field
Solving for the field,
If the field is not uniform, it can be calculated at multiple points:

10. 1. moves toward A with an increasing speed.
A proton is released from rest at point B, where the potential is 0 V. Afterward, the proton
1. moves toward A with an increasing speed.
2. moves toward A with a steady speed.
3. remains at rest at B.
4. moves toward C with a steady speed.
5. moves toward C with an increasing speed.
STT29.3

11. Equipotential Lines
An equipotential is a line or surface over which the potential is constant.
Electric field lines are perpendicular to equipotentials.
The surface of a conductor is an equipotential.

12. How strong is the electric field between two parallel plates 5
How strong is the electric field between two parallel plates 5.8 mm apart if the potential difference between them is 220 V?

13. Electric Potential Due to Point Charges
Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector.

14. Equipotential Lines

15. Electric Potential Due to Point Charges
These plots show the potential due to
positive and
(b) negative charge.

16. A dipole , is a pair of opposite charges Q, -Q separated by a distance d.

17. The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.

18. Electric Potential Due to Point Charges
The electric potential due to a point charge can be derived using calculus.

19. Rank in order, from largest to smallest, the potential differences ∆V12, ∆V13, and ∆V23 between points 1 and 2, points 1 and 3, and points 2 and 3.
1. ∆V12 > ∆V13 = ∆V23
2. ∆V13 > ∆V12 > ∆V23
3. ∆V13 > ∆V23 > ∆V12
4. ∆V13 = ∆V23 > ∆V12
5. ∆V23 > ∆V12 > ∆V13
STT29.5

20. Using potential differences:
From U = qV (potential energy = chargepotential) we get U = q V.
If 500 J of work is required to carry a 40 C charge from one point to another, the potential difference between the two points is V
2. 20,000 V V
4. depends upon the path

21. An electron is accelerated from rest through a potential difference V
An electron is accelerated from rest through a potential difference V. Its final speed is proportional to
1. V
2. V 2
3. V 1/2
4. 1/V
5. 1/V ½
6. You need to know the x dependence of V(x)

22. U = q V.
During a lightning discharge, 30 C of charge move through a potential difference of 1.0108 V in 0.02 s. The energy released by this lightning bolt is
1. 1.51011 J
2. 3.0109 J
3. 6.0107 J
4. 3.3106 J J

23. The equipotential surfaces associated with an isolated point charge are
1. radially outward from the charge
2. vertical planes
3. horizontal planes
4. concentric spheres centered on the charge
5. concentric cylinders with the charge on the axis

24. A point charge Q creates an electric potential of 125 volts at a distance of 15 cm. What is Q?

25. If two points are at the same potential, does this mean that no work is done in moving a test charge from one point to the other? Does this imply that no force need be exerted? Explain.
If two points are at the same potential, then no NET work was done in moving a test charge from one point to the other. Along some segments of the path, some positive work might have been done, but along other segments of the path, negative work would then have been done. And if the object was moved along an equipotential line, then no work would have been done along any segment of the path.

26. Can a particle ever move from a region of low electric potential to one of high potential and yet have its electric potential energy decrease? Explain.
A negative particle will have its electric potential energy decrease if it moves from a region of low electric potential to one of high potential. If the charge is negative and the potential difference is positive, the change in potential energy will be negative, and so decrease.

27. How much kinetic energy will an electron gain (in joules and eV) if it accelerates through a potential difference of 23,000 V in a TV picture tube?
The kinetic energy gained is equal to the work done on the electron by the electric field. The potential difference must be positive for the electron to gain potential energy

28. The work done by an external force to move a charge of -850 μC from point a to point b is 1.5x10-3 J. If the charge was started from rest and had of kinetic energy of 4.82x10-4J when it reached point b, what must be the potential difference between a and b?

29. Use your understanding of the mathematical relationship between work, potential energy, charge and electric potential difference to complete the following statements:
a. A 9-volt battery will increase the potential energy of 1 coulomb of charge by ____ joules.
b. A 9-volt battery will increase the potential energy of 2 coulombs of charge by ____ joules.
c. A 9-volt battery will increase the potential energy of 0.5 coulombs of charge by ____ joules.
d. A ___-volt battery will increase the potential energy of 3 coulombs of charge by 18 joules.
e. A ___-volt battery will increase the potential energy of 2 coulombs of charge by 3 joules.
f. A 1.5 volt battery will increase the potential energy of ____ coulombs of charge by 0.75 joules.
g. A 12 volt battery will increase the potential energy of ____ coulombs of charge by 6 joules. 9 18
4.5 6
1.5
0.5
0.5

30. Potential Due to Electric Dipole; Dipole Moment
The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly.

31. Potential Due to Electric Dipole; Dipole Moment
Approximation for potential far from dipole:

32. Potential Due to Electric Dipole; Dipole Moment
Or, defining the dipole moment p = Ql,

33. An electron and a proton are 0. 53 angstroms apart
An electron and a proton are 0.53 angstroms apart. What is their dipole moment if they are at rest?
The dipole moment is the product of the magnitude of one of the charges times the separation distance.

34. Capacitance
A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

35. Capacitance
Parallel-plate capacitor connected to battery. (b) is a circuit diagram.

36. Capacitance
When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V

37. The two plates of a capacitor hold opposite charges of magnitude 2500μC of charge, respectively, when the potential difference is 850 V. What is the capacitance?

38. Capacitance
The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor.
For a parallel-plate capacitor:

39. If a capacitor has opposite charges of 5
If a capacitor has opposite charges of 5.2μC on the plates, and an electric field of 2kV/mm is desired between the plates, what must each plate’s area be?

40. Dielectrics
A dielectric is an insulator, and is characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled with dielectric:

41. Dielectrics
The molecules in a dielectric tend to become oriented in a way that reduces the external field.

42. Induced polarization of dielectric opposes E0
Net electric field
electric field if no dielectric

43. Dielectrics
This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.

44. Dielectrics
Dielectric strength is the maximum field a dielectric can experience without breaking down.

45. What is the capacitance of two square parallel plates 5
What is the capacitance of two square parallel plates 5.5 cm on a side that are separated by 1.8 mm of paraffin? Paraffin has a dielectric constant 2.2 times that of air (free space).

46. If all linear dimensions (length, width, height and plate separation) of a parallel plate capacitor are tripled while the shape of the plates remains the same, the capacitance is
multiplied by 3
multiplied by 9
multiplied by 27
stays the same
divided by 3

47. Storage of Electric Energy
A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.

48. How does the energy stored in a capacitor change if (a) the potential difference is doubled, and (b) the charge on each plate is doubled, as the capacitor remains connected to a battery?
(a) PE = ½ CV2 so if C is constant the energy increases by a factor of 4.
(b) The potential difference is constant, so PE = ½ QV. Doubling the charge will double the potential energy.

49. Storage of Electric Energy
The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field:
The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!

50. Storage of Electric Energy
Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives.

51. A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this device is charged to 5.0 kV and stores 1200 J of energy. What is its capacitance?

52. A parallel-plate capacitor is charged to a potential difference of 100 V and then disconnected from the source. A slab of dielectric is then inserted between the plates. Which of the following changes?
100 V
Just 1 and 2
Just 1 and 3
Just 2 and 3 4
The potential difference
The capacitance
The charge on the plates
All of the above
10/3 dielectrics (5)

53. +q +q D d -q -q
10/17 energy stored in capacitance

54. +q +q -q -q
10/17 energy stored in capacitance

55. V V
10/17 energy stored in capacitance

56. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
A cathode ray tube contains a wire cathode that, when heated, emits electrons. A voltage source causes the electrons to travel to the anode.

57. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
The electrons can be steered using electric or magnetic fields.

58. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
Televisions and computer monitors (except for LCD and plasma models) have a large cathode ray tube
as their display. Variations in the field steer the electrons on their way to the screen.

59. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
An oscilloscope displays en electrical signal on a screen, using it to deflect the beam vertically while it sweeps horizontally.

60. The Electrocardiogram (ECG or EKG)
The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart.

61. Which is more dangerous, touching a faulty 110-volt light bulb or a Van de Graaff generator charged to 100,000 volts? Why?
Touching the Van de Graaff generator may be a hair-raising experience, but touching the 110-volt faulty fixture could be the last thing you do. Electric potential is electric potential energy per charge. Although the generator may be charged to an electric potential of 100,000 volts the amount of charge is relatively small. That and the short time of charge transfer is why you're normally not harmed when it discharges through you. In contrast, if you become the short-circuit for household 110 volts, the sustained transfer of charge is appreciable. Less energy per charge, but many, many more charges!

62. Summary of Chapter Electric potential energy:
Electric potential difference: work done to move charge from one point to another
Relationship between potential difference and field:

63. Summary of Chapter 17
Equipotential: line or surface along which potential is the same
Electric potential of a point charge:
Electric dipole potential:

64. Summary of Chapter 17
Capacitor: nontouching conductors carrying equal and opposite charge
Capacitance:
Capacitance of a parallel-plate capacitor:

65. Summary of Chapter 17 A dielectric is an insulator
Dielectric constant gives ratio of total field to external field
Energy density in electric field:

66. Internet Archive: Details: Physics B Lesson 34: Capacitors