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Physics II: Electricity & Magnetism

Physics II: Electricity & Magnetism. Sections 23.6 & 23.9. Wednesday (Day 9). 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 =∞.

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Physics II: Electricity & Magnetism

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  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 www.plutonium-239.com

  4. 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? C A B NOA NOB P NOC N O

  5. 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 Q1B Q1A Q1C O

  6. 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. 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 HOW DO WE DETERMINE THE ELECTRIC POTENTIAL OF AN ELECTRIC DIPOLE? Vocabulary

  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. 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 L/2 p L/2 q

  13. 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 L/2 p 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. 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 10-11 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 10-30 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 10-10 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. 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 10-11 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 10-30 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. 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 10-11 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 10-30 C•m. Calculate (b) the effective charge q on each H. 104.5º

  18. 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 10-11 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 10-30 C•m. Calculate (c) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom (q = 180º). 104.5º

  19. 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 10-11 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 10-30 C•m. Calculate (c) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom (q = 180º). 104.5º

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

  21. 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 10-11 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 10-30 C•m. Calculate (c) the potential 9.0 x 10-10 m from the dipole along its axis, with oxygen being the nearer atom (q = 180º). 104.5º

  22. 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 10-11 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 10-30 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 = -1.04 x 10-19 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. 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 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 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. 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. 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. 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. 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. 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. 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. HOW DO WE APPLY ELECTRIC POTENTIAL TO VARIOUS APPLICATIONS? Electric Potentials in Technology • Van de Graaff Accelerator • Produces highly energetic charged particles

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

  32. 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. 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 10-10 m and the dipole moment of this group is about 8.0 x 10-30 Cm. Calculate (a) the effective charge Q on the C and O atoms, and (b) the potential 9.0 x 10-10 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. 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.

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