1. Physics II: Electricity & Magnetism
Sections 23.6 & 23.9

2. Wednesday (Day 9)

3. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Warm-Up
Thurs, Mar 12
Calculate the electric potential at points A, B, and C due to the charges shown. Assume V=0 at r=∞.
What is the length difference between
rb & ra?
rb & rc?
What are the angles for NOA, NOB, and NOC?
Place your homework on my desk: (If Applicable)
Web Assign Problems (except for 23.10, 23.14, 23.15)
For future assignments - check online at

4. Application: Potential at various locations around two charges
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application: Potential at various locations around two charges
Calculate the electric potential at points A, B, and C due to the charges shown. Assume V=0 at r=∞.
What is the length difference between
rb & ra?
rb & rc?
What are the angles for NOA, NOB, and NOC? A B C
NOA
NOB P
NOC N O

5. Application: Potential at various locations around two charges
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application: Potential at various locations around two charges
Calculate the electric potential at points A, B, and C due to the charges shown. Assume V=0 at r=∞.
What is the difference between the radii of
Q2A, OA, Q1A?
Q2B, OB, Q1B?
Q2C, OC, Q1C?
What are the angles for Q1C, Q1B, and Q1A ? C
Q1A
Q1B
Q1C O

6. Essential Question(s)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Essential Question(s)
HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?
How do we determine the electric potential of an electric dipole?

7. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Vocabulary
Electric Potential
Potential
Difference in Potential
Potential Difference
Volt
Voltage
Equipotential Lines
Equipotential Surfaces
Electric Dipole
Dipole Moment
Electron Volt
Cathode Ray Tube
Thermionic Emission
Cathode
Anode
Cathode Rays
Oscilloscope

8. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Agenda
Electric Dipoles
Derivation #1: Approximation Method
Derivation #2: Exact Method using the Law of Cosines
Determine the Percent Difference for the Approximation Method (Excel Spreadsheet)
Electron Volt
Applications of Potential
Complete the following
Lab #5: Potential
Web Assign Problems 23.10, 23.14, & 23.15

9. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Electric Dipoles
Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l.
The dipole moment, p: The quantity
p=Ql where Q is always defined as positive, q+.
q-= p / l cos= p / l cos(180º) = –p / l
The dipole moment points from the negative to the positive charge.
Many molecules have a dipole moment and are referred to as polar molecules.
It is interesting to note that the value of the separated charges may be less than that of a single electron or proton, but they cannot be isolated.

10. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Potential due to an Electric Dipole
The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly. However, this requires the use the law of cosines and is a very large equation for a single dipole.
By using an approximation method, a simplistic equation can be derived to calculate the potential at distances much greater than the length of the dipole moment.

11. HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?
Potential due to an Electric Dipole
*Approximation for determining potential far from dipole:
*Refer to the “Electric Potential due to an Electric Dipole” handout for full details regarding its derivation.

12. Potential due to an Electric Dipole
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Potential due to an Electric Dipole
Using the Law of Cosines (Appendix A-3), r+ and r- can be determined from  and : D r r r   q p
L/2
L/2 q

13. Potential due to an Electric Dipole
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Potential due to an Electric Dipole
To determine V at point D: D r r r
By substituting in r+ and r- into the equation above, we get   q p
L/2
L/2 q

14. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Electric Dipoles
Use Excel to compare the percent difference between the accurate method and approximate method

15. Application of Electric Dipole Potentials
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(a) the effective charge q on the O atom.
(b) the effective charge q on each H.
(c) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º).
(d) What would the potential be at this point if only the oxygen (O) were charged?
104.5º

16. Application of Electric Dipole Potentials (Part A)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part A)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(a) the effective charge q on the O atom.
104.5º
Although this charge is less than e, the smallest known charge, it is not a charge that can be isolated, but is the effective charge that results from unequal sharing of the electrons.

17. Application of Electric Dipole Potentials (Part B)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part B)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(b) the effective charge q on each H.
104.5º

18. Application of Electric Dipole Potentials (Part C - Approx.)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part C - Approx.)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(c) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º).
104.5º

19. Application of Electric Dipole Potentials (Part C - Exact)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part C - Exact)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(c) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º).
104.5º

20. Application of Electric Dipole Potentials (Part C - Exact)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part C - Exact)
104.5º

21. Application of Electric Dipole Potentials (Part C - Exact)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part C - Exact)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m. Calculate
(c) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º).
104.5º

22. Application of Electric Dipole Potentials (Part D)
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials (Part D)
The dipole moment, considered as a vector, point from the negative to the positive charge. The water molecule (shown) has a dipole moment p which can be considered as the vector sum of the two dipole moments, p1 and p2 as shown. The distance, LOH, between the hydrogen (+) and oxygen (-) atoms is about 9.57 x m; the lines joining the center of the O atom with each H atom make an angle, 2, of 104.5º and the net dipole moment, pnet, has been measured to be 6.1 x C•m.
(d) What would the potential be at this point if only the oxygen (O) were charged?
104.5º
If we assume that the oxygen has charge Q = x C, as in part a above, and that the carbon is not charged, we use the formula for a single charge:
Of course, we expect the potential of a single charge to have a greater magnitude than that of a dipole of equal charge at the same distance.

23. Application of Electric Dipole Potentials
HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Application of Electric Dipole Potentials
The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen (-) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x m and the dipole moment of this group is about 8.0 x Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?

24. Essential Question(s)
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Essential Question(s)
HOW DO WE DESCRIBE AND APPLY THE CONCEPT OF ELECTRIC POTENTIAL?
How do we apply electric potential to various applications?

25. The Electron Volt, a Unit of Energy
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy an electron gains when it is accelerated though a potential difference of one volt.
Electron volts are useful in atomic, nuclear, and particle physics.

26. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
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.

27. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
The electrons can be steered using electric or magnetic fields.

28. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
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.

29. Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
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.

30. Electric Potentials in Technology
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Electric Potentials in Technology
Van de Graaff Accelerator
Produces highly energetic charged particles

31. Electric Potentials in Technology
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Electric Potentials in Technology
Field-Ion Microscope
Images of individual atoms

32. Electric Potentials in Technology
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Electric Potentials in Technology
Xerography
Relatively cheap way to make copies of anything that will fit on the glass

33. Electric Potentials in Technology
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
Electric Potentials in Technology
Scanning Tunneling Microscope
Can image individual atoms
Can also move single atoms to make desired configuration

34. HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE?
Summary
The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen ( -) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x m and the dipole moment of this group is about 8.0 x Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x m from the dipole along its axis, with oxygen being the nearer atom (q = 180º). (c) What would the potential be at this point if only the oxygen (O) were charged?
HW (Place in your agenda):
Web Assign 23.? - 23.?
Future assignments:
Lab #5: Potential Lab Report (Due in 5 classes)

35. The Electrocardiogram (ECG or EKG)
HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS?
The Electrocardiogram (ECG or EKG)
The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart.