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Chapter 30. Potential and Field 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 30. 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 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 30. Reading Quizzes Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What quantity is represented by the symbol ? A. Electronic potential B. Excitation potential C. EMF D. Electric stopping power E. Exosphericity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What quantity is represented by the symbol ? A. Electronic potential B. Excitation potential C. EMF D. Electric stopping power E. Exosphericity Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the SI unit of capacitance? A. Capaciton B. Faraday C. Hertz D. Henry E. Exciton Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What is the SI unit of capacitance? A. Capaciton B. Faraday C. Hertz D. Henry E. Exciton Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. This chapter investigated A. B. C. D. E. parallel capacitors perpendicular capacitors series capacitors. Both a and b. Both a and c. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. This chapter investigated A. B. C. D. E. parallel capacitors perpendicular capacitors series capacitors. Both a and b. Both a and c. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 30. Basic Content and Examples Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding the Potential from the Electric Field The potential difference between two points in space is where s is the position along a line from point i to point f. That is, we can find the potential difference between two points if we know the electric field. We can think of an integral as an area under a curve. Thus a graphical interpretation of the equation above is Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Finding the potential from the electric field Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.2 The potential of a parallelplate capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.2 The potential of a parallelplate capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.2 The potential of a parallelplate capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.2 The potential of a parallelplate capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.2 The potential of a parallelplate capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding the Electric Field from the Potential In terms of the potential, the component of the electric field in the s-direction is Now we have reversed Equation 30.3 and have a way to find the electric field from the potential. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.4 Finding E from the slope of V Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Capacitance and Capacitors The ratio of the charge Q to the potential difference ΔVC is called the capacitance C: Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing. The SI unit of capacitance is the farad: 1 farad = 1 F = 1 C/V. The charge on the capacitor plates is directly proportional to the potential difference between the plates. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.6 Charging a capacitor QUESTIONS: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.6 Charging a capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.6 Charging a capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.6 Charging a capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Combinations of Capacitors If capacitors C1, C2, C3, … are in parallel, their equivalent capacitance is If capacitors C1, C2, C3, … are in series, their equivalent capacitance is Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.9 Storing energy in a capacitor QUESTIONS: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.9 Storing energy in a capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 30.9 Storing energy in a capacitor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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/m3. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 30. Summary Slides Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 30. Clicker Questions Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which potential-energy graph describes this electric field? Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which potential-energy graph describes this electric field? Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which set of equipotential surfaces matches this electric field? Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which set of equipotential surfaces matches this electric field? Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. B. C. D. E. V1 = V2 = V3 and E1 > E2 > E3 V1 > V2 > V3 and E1 = E2 = E3 V1 = V2 = V3 and E1 = E2 = E3 V1 > V2 > V3 and E1 > E2 > E3 V3 > V2 > V1 and E1 = E2 = E3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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. B. C. D. E. V1 = V2 = V3 and E1 > E2 > E3 V1 > V2 > V3 and E1 = E2 = E3 V1 = V2 = V3 and E1 = E2 = E3 V1 > V2 > V3 and E1 > E2 > E3 V3 > V2 > V1 and E1 = E2 = E3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the equivalent capacitance (Ceq)a to (Ceq)d of circuits a to d. A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the equivalent capacitance (Ceq)a to (Ceq)d of circuits a to d. A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.