Chapter 16

1. Chapter 16 Conceptual questions: 5,7,13 Quick quizzes: 2,3,4,6 Problems: 1,11,34,43 Examples: 1,3,6,7,8 Electric Energy and Capacitance

2. Work and Potential Energy • The electrostatic force is a conservative force • As the charge moves from A to B, work is done in it • W = F d= q E d • ΔPE = - W = - q E d • only for a uniform field

3. Potential Difference • The potential difference between points A and B is defined • ΔV = VB – VA = ΔPE / q • Potential difference is not the same as potential energy • Units of potential difference V = J/C

4. Electric Potential of a Point Charge • The potential created by a point charge q at any distance r from the charge is unit: 1 volt = 1 J/C

5. Electrical Potential Energy of Two Charges • V1 is the electric potential due to q1 at some point P1 • The work required to bring q2 from infinity to P1 without acceleration is q2V1 • This work is equal to the potential energy of the two particle system

6. Problem Solving with Electric Potential (Point Charges) • Remember that potential is a scalar quantity • So no components to worry about • Use the superposition principle when you have multiple charges • Take the algebraic sum • Keep track of sign • The potential is positive if the charge is positive and negative if the charge is negative • Use the basic equation V = keq/r

7. Conceptual questions 5. Suppose you are sitting in a car and a 20,000-volt power line drops across the car. Should you stay in the car or get out? The power line potential is 20,000 V compared to the potential of the ground. 7. Explain why, under static conditions, all points in a conductor must be at the same electric potential.

8. QUICK QUIZ 16.3 If the electric potential at some point is zero, you can conclude that (a) The electric field is zero at this point(b) no charges exist in the vicinity of that point, (c) some charges are positive and some are negative, or (d) all charges in the vicinity have the same sign.

9. QUICK QUIZ 16.4 A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a larger volume while the charged particle remains at the center, which of the following changes? (a) the electric potential at the surface of the balloon, (b) the magnitude of the electric field at the surface of the balloon.

10. Potentials and Charged Conductors • Work required to move a charge between two points is given by • W = -q(VB – VA) • When the two points that are at the same electric potential • when VA = VB W = 0 • All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential

11. Problem 16-1 A proton moves 2.00 cm parallel to the electric field of E=200 N/C. How much work is done by thefield on the proton? What change occurs in the potential energy of the proton? What potential difference did the proton move through?

12. Conductors in Equilibrium • The conductor has an excess of positive charge • All of the charge resides at the surface • E = 0 inside the conductor • The electric field just outside the conductor is perpendicular to the surface • The potential is a constant everywhere on the surface of the conductor • The potential everywhere inside the conductor is constant and equal to its value at the surface

13. The Electron Volt • The electron volt (eV) is defined as the energy that an electron (or proton) gains when accelerated through a potential difference of 1 V • Electrons in normal atoms have energies of 10’s of eV • Excited electrons have energies of 1000’s of eV • High energy gamma rays have energies of millions of eV • 1 eV = 1.6 x 10-19 J

14. Equipotentials and Electric Fields Lines -- Positive Charge • The equipotentials for a point charge are a family of spheres centered on the point charge • The field lines are perpendicular to the electric potential at all points

15. Equipotentials and Electric Fields Lines -- Dipole • Equipotential lines are shown in blue • Electric field lines are shown in red • The field lines are perpendicular to the equipotential lines at all points

16. The Xerographic Process

17. Problem 16-11 a. Find the potential 1.00 cm from a proton. b. What is the potential difference between two points that are 1.00 cm and 2.00 cm from a proton?

18. Capacitance • The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates) • Units: Farad (F) • 1 F = 1 C / V • A Farad is very large • Often will see µF or pF

19. Parallel-Plate Capacitor • For a parallel-plate capacitor whose plates are separated by air:

20. 16-43 • A parallel plate capacitor has 2.00 cm2 plates that are separated by 5.00 mm with air between them. If a 12.0 V battery is connected to this capacitor, how much energy does it store?

21. Applications of Capacitors -- Computers • Computers use capacitors in many ways • Some keyboards use capacitors at the bases of the keys • When the key is pressed, the capacitor spacing decreases and the capacitance increases • The key is recognized by the change in capacitance

22. Capacitors in Parallel • The total charge is equal to the sum of the charges on the capacitors • Qtotal = Q1 + Q2 • The potential difference across the capacitors is the same

23. Capacitors in Parallel • The capacitors can be replaced with one capacitor with a capacitance of Ceq • The equivalent capacitor must have exactly the same external effort on the circuit as the original capacitors Ceq = C1 + C2

24. Capacitors in Series • An equivalent capacitor can be found that performs the same function as the series combination • The potential differences add up to the battery voltage

25. QUICK QUIZ 16.6 A capacitor is designed so that one plate is large and the other is small. If the plates are connected to a battery, (a) the large plate has a greater charge than the small plate, (b) the large plate has less charge than the small plate, or (c) the plates have charges equal in magnitude but opposite in sign.

26. Energy Stored in a Capacitor • Energy stored = ½ Q ΔV • From the definition of capacitance, this can be rewritten in different forms

27. Problem 16-34 Consider the combination of capacitors in the figure. What is the equivalent capacitance of the group? Determine the charge on each capacitor.

28. Solution, P.16.34 From the second figure we find From the first figure

29. Capacitors with Dielectrics • A dielectric is an insulating material that, when placed between the plates of a capacitor, increases the capacitance • Dielectrics include rubber, plastic, or waxed paper • C = κCo = κεo(A/d) • The capacitance is multiplied by the factor κ when the dielectric completely fills the region between the plates

30. Capacitors with Dielectrics

31. Atomic Description • The presence of the positive charge on the dielectric effectively reduces some of the negative charge on the metal • This allows more negative charge on the plates for a given applied voltage • The capacitance increases

32. Conceptual question 16-13 • What happens to the charge of a capacitor if the potential difference between its plates is doubled? • What happens to the energy stored in a capacitor if the plate separation is doubled while the charge on the capacitor remains constant?

33. Dipole moment of a water molecule We use symbols p or m to denote dipole. Remember, dipole is a vector quantity p=qd or m=qd Bond dipoles add as vectors to form a resultant dipole.

34. Dipole moment of carbon dioxide molecule C O O The C=O bonds are polar, but antiparallel, so their effects are cancelled. The net molecular dipole of CO2 is zero.

35. MCAT 1. Which of the following is a vector quantity? a. electric charge c. electric power b. electric energy d. electric field intensity 2. What is the potential difference between point A and B if 10 J work is required to move a charge of 4.0 C from one point to another? a. 0.4 V b. 2.5 V c. 14 V d. 40 V 3. How much work is require to move an electron between two terminals whose potential difference is 2.0 x 106 V? a. 3.2 x 10-13 J b. 8.0 x 10-26 J c. 1.25 x 1025 J d. 8.0 x 10-13 J