Homework Reading: Chap. 29, Chap. 31 and Chap. 32 Suggested exercises: 29.17, 29.19, 29.22, 29.23, 29.24, 29.26, 29.27, 29.29, 29.30, 29.31, 29.32 Problems: 29.49, 29.51, 29.52, 29.57, 29.58, 29.59, 29.63, 29.69, 29.70, 29.72, 29.80, 29.81 (due Oct. 26, 2015) Chapter 29. Capacitance and Dielectrics To understand the production of electricity by solar cells or batteries, we must first address the connection between electric potential and electric field. Chapter Goal: To understand how the electric potential is connected to the electric field. 1
Chapter 29. Potential and Field Topics: Connecting Potential and Field Sources of Electric Potential Finding the Electric Field from the Potential A Conductor in Electrostatic Equilibrium Capacitance and Capacitors The Energy Stored in a Capacitor Dielectrics Chapter 29. Basic Content and Examples 2
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Inside a Computer Chip The potential of two parallel-plates +Q -Q 4
Conducting Spheres a b d c Similarity 5
Similarity Put the same amount of water V into two different containers, one has cross-sectional area of A 1, one is A 2. The height of the water in containers are A 1 Gravitational potential energy: A 2 Similarity +Q -Q V ha Q VC V / h A Q/ V C 6
Capacitor & Capacitance: Definition Two charged objects at different electric potential, V, produce an electric field. For fixed geometry, one can describe the problem with one variable, E, V, or Q The geometry can be described in terms of capacitance. Units: C Q/ V Charge Coulombs; Potential Volts; Capacitance Farads. Capacitor & Capacitance: Definition C > 0 depends only on the geometry of the device. Describing the ability to store charges. 7
Parallel Plate Capacitor +Q -Q 8
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Charging a Capacitor - --- - - - - + + + - + External work needs to be done in order to charge a capacitor! 10
Battery Batteries and emf The potential difference between the terminals of an ideal battery is In other words, a battery constructed to have an emf of 1.5V creates a 1.5 V potential difference between its positive and negative terminals. The total potential difference of batteries in series is simply the sum of their individual terminal voltages: 11
Kirchhoff s Loop Law For any path that starts and ends at the same point Stated in words, the sum of all the potential differences encountered while moving around a loop or closed path is zero. This statement is known as Kirchhoff s loop law. Kirchhoff s Loop Law 12
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Combinations of Capacitors If capacitors C 1, C 2, C 3, are in parallel, their equivalent capacitance is If capacitors C 1, C 2, C 3, are in series, their equivalent capacitance is 14
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The Energy Stored in a Capacitor Capacitors are important elements in electric circuits because of their ability to store energy. The charge on the two plates is ±q and this charge separation establishes a potential difference ΔV = q/c between the two electrodes. In terms of the capacitor s potential difference, the potential energy stored in a capacitor is The Energy in the Electric Field The energy density of an electric field, such as the one inside a capacitor, is The energy density has units J/m 3. 20
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Figure shows a parallel plate capacitor of plate area A and plate separation d. A potential difference V 0 is applied between the plates. The battery is then disconnected, and a dielectric slab of thickness b and dielectric constant is placed between the plates as shown. Assume A = 115 cm 2 d = 1.24 cm V 0 = 85.5 V b = 0.78 cm = 2.61 (a)what is the capacitance C 0 before the dielectric slab is inserted? (b) What free charge appears on the plates? (c) What is the electric field E 0 in the gaps between the plates and the dielectric slab? 23
(d) What is the electric field E 1 in the dielectric slab? (e) What is the potential difference V between the plates after the slab has been introduced? (f) What is the capacitance with the slab in place? What will be the capacitance? 1 2 1 2 24
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Dielectrics The dielectric constant, like density or specific heat, is a property of a material. Easily polarized materials have larger dielectric constants than materials not easily polarized. Vacuum has κ = 1 exactly. Filling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant. 26
Chapter 29. Summary Slides General Principles 27
General Principles General Principles 28
Important Concepts Important Concepts 29
Applications Applications 30
Chapter 29. Clicker Questions What total potential difference is created by these three batteries? A. 1.0 V B. 2.0 V C. 5.0 V D. 6.0 V E. 7.0 V 31
What total potential difference is created by these three batteries? A. 1.0 V B. 2.0 V C. 5.0 V D. 6.0 V E. 7.0 V Which potential-energy graph describes this electric field? 32
Which potential-energy graph describes this electric field? Which set of equipotential surfaces matches this electric field? 33
Which set of equipotential surfaces matches this electric field? Three charged, metal spheres of different radii are connected by a thin metal wire. The potential and electric field at the surface of each sphere are V and E. Which of the following is true? A. V 1 = V 2 = V 3 and E 1 > E 2 > E 3 B. V 1 > V 2 > V 3 and E 1 = E 2 = E 3 C. V 1 = V 2 = V 3 and E 1 = E 2 = E 3 D. V 1 > V 2 > V 3 and E 1 > E 2 > E 3 E. V 3 > V 2 > V 1 and E 1 = E 2 = E 3 34
Three charged, metal spheres of different radii are connected by a thin metal wire. The potential and electric field at the surface of each sphere are V and E. Which of the following is true? A. V 1 = V 2 = V 3 and E 1 > E 2 > E 3 B. V 1 > V 2 > V 3 and E 1 = E 2 = E 3 C. V 1 = V 2 = V 3 and E 1 = E 2 = E 3 D. V 1 > V 2 > V 3 and E 1 > E 2 > E 3 E. V 3 > V 2 > V 1 and E 1 = E 2 = E 3 Rank in order, from largest to smallest, the equivalent capacitance (C eq ) a to (C eq ) d of circuits a to d. A. (C eq ) d > (C eq ) b > (C eq ) a > (C eq ) c B. (C eq ) d > (C eq ) b = (C eq ) c > (C eq ) a C. (C eq ) a > (C eq ) b = (C eq ) c > (C eq ) d D. (C eq ) b > (C eq ) a = (C eq ) d > (C eq ) c E. (C eq ) c > (C eq ) a = (C eq ) d > (C eq ) b 35
Rank in order, from largest to smallest, the equivalent capacitance (C eq ) a to (C eq ) d of circuits a to d. A. (C eq ) d > (C eq ) b > (C eq ) a > (C eq ) c B. (C eq ) d > (C eq ) b = (C eq ) c > (C eq ) a C. (C eq ) a > (C eq ) b = (C eq ) c > (C eq ) d D. (C eq ) b > (C eq ) a = (C eq ) d > (C eq ) c E. (C eq ) c > (C eq ) a = (C eq ) d > (C eq ) b Chapter 30. Reading Quizzes 36
What quantity is represented by the symbol? A. Electronic potential B. Excitation potential C. EMF D. Electric stopping power E. Exosphericity What quantity is represented by the symbol? A. Electronic potential B. Excitation potential C. EMF D. Electric stopping power E. Exosphericity 37
What is the SI unit of capacitance? A. Capaciton B. Faraday C. Hertz D. Henry E. Exciton What is the SI unit of capacitance? A. Capaciton B. Faraday C. Hertz D. Henry E. Exciton 38
The electric field A. is always perpendicular to an equipotential surface. B. is always tangent to an equipotential surface. C. always bisects an equipotential surface. D. makes an angle to an equipotential surface that depends on the amount of charge. The electric field A. is always perpendicular to an equipotential surface. B. is always tangent to an equipotential surface. C. always bisects an equipotential surface. D. makes an angle to an equipotential surface that depends on the amount of charge. 39
This chapter investigated A. parallel capacitors B. perpendicular capacitors C. series capacitors. D. Both a and b. E. Both a and c. This chapter investigated A. parallel capacitors B. perpendicular capacitors C. series capacitors. D. Both a and b. E. Both a and c. 40