Chapter 21 Electric Potential Topics: • • • • Conservation of energy Work and Delta PE Electric potential energy Electric potential Sample question: Shown is the electric potential measured on the surface of a patient. This potential is caused by electrical signals originating in the beating heart. Why does the potential have this pattern, and what do these measurements tell us about the heart s condition? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 What to do to do well in this class A. Focus on key physics concepts • May seem like basics but will help you solve even complex problems • Focus on principle rather than recipes • Need to have a functional understanding of key concepts • Express key equations as sentences • Know where they come from and what they mean • Know how and when to apply them • Know which equations are general and which are special cases • Must know when not to apply special cases • Look at a problem after a good physics diagram and maybe a good physical diagram and know what key physics concepts apply in that problem • Memorize key concepts so you can look at a problem, say that s Newton 2, and know the associated equation in a snap Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 What to do to do well in this class A. Focus on key physics concepts • How to do this • When you look at problems, mentally group problems by the physics rather than the physical situation • After each class or at least each week, create a notesheet to organize a structure of the new key concepts for each chapter and note how they fit in with previous key concepts • Use the note sheet to do homework problems (a) do as many homework problems as you can just using this sheet. (b) then go to your notes and the textbook for your missing pieces • Use flash cards to memorize key concepts - include the concept description, relevant equations, diagrams, and what types of problems benefit from using that concept • Pay close attention to examples done in class and note the physics and assume/observes in each example and how these are used Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Types of Energy Conservation of Energy Equation (key concept) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Chapter 21 Key Ideas (Physics 151) Dot Product Method for multiplying two vectors to get a scalar Definition of Work Work is how forces add energy to or take away energy from a system. It is the effect of a force applied over a displacement. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work ! ! ! ! Work!!W = F!i!!r = F !r cos " Where ! = angle between the vectors Work- Energy Theorem (only valid when particle model applies) Wnet = !KE Work done by a conservative force (Fg, Fs, & Fe) Wg = !"PEg Also work done by conservative force is path independent Conservation of Energy Equation KEi + ! PEi + " Esys = KE f + different !types Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. ! PE f + "Eth different !types Slide 21-16 Energy Bar Graph Sample Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example 1 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example II Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example III Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Review of Work ! ! ! ! Definition of Work: Work!!W = F!i!!r = F !r cos " where ! = angle between the vectors • Calculate the work done in moving each ball from y = 0 meters to y = 5 meters • Calculate the work per kg for moving each ball from y = 0 m to 5 m • Calculate the change in gravitational potential energy per kg for moving each ball from = 0 m to 5 m • Calculate the speed each ball would have as it reached the ground if released from 5 meters above the ground Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-9 Electric Potential Energy Case A - Book starts & stops at rest WNet = !EK = 0J Whand + Wg = 0 ! Whand = "Wg = #Eg Case C - Charge at rest at A and B WNet = !EK = 0J Whand + We = 0 ! Whand = "We = #Ee Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-9 Electric potential energy: A qualitative analysis • A positively charged cannonball is held near another fixed positively charged object in the barrel of the cannon. • Some type of energy must decrease if gravitational and kinetic energies increase in this process. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 q1q2 PEe = k r12 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart) D Potential Energy for a uniform infinite plate ! ! % !PEe = "We = " & Fe # !r cos $ '( = " ( q E ) !r cos $ For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or inbetween the two plates Electric Potential V and Change in Electric Potential => Delta V Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Graphing the electric potential energy versus distance • Because of the 1/r dependence, the electric potential energy approaches positive infinity when the separation approaches zero, and it becomes less positive and approaches zero as like charges are moved far apart. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Electric Potential Energy A cart on a track has a large, positive charge and is located between two sheets of charge. Initially at rest at point A, the cart moves from A to C. a. Draw qualitative force diagrams for the cart at positions A, B and C. b. Draw qualitative energy bar charts for the cart when it is at each position A, B and C. List the objects that make up your system: c. How would your force and energy diagrams change (if at all) if the sheet to the right were also positively charged? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy - Delta PEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) (a) Greatest Delta PEe (b) (c) (d) Hydrogen Atom Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy – Delta PEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) (e) (f) Greatest Delta PEe (g) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy – Delta PEe Is the change ∆PEe of a + charged particle positive, negative, or zero as it moves from i to f? (a) Positive (b) Negative (c) Zero (d) Can t tell Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11 Electric Potential Model Worksheet 2: Energy and Potential in Uniform Fields " Rank the change in gravitational potential energy for the following lettered objects in the Earth s gravitational field. a. . most _______ _________ ________ ________ _______ _______ ________ b. Explain your ranking, stating why each is greater than, less than, or equal to its neighbors. c. Where is the energy stored? What gains or loses energy as the masses move from one place to another? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. a. Draw several electric field lines in the region between the plates. b. Determine the change in electrical potential energy in moving a positive 4 microCoulomb charge from A to B. c. Determine the change in electrical potential energy in moving a negative 12 microCoulomb charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth a. Draw several gravitational field lines in the region around Earth. b. Determine the change in gravitational potential energy when the spacecraft moves from A to B, where A is 10 million miles from Earth and B is 30 million miles from Earth. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. a. Draw several electric field lines in the region around the source charge. b. Determine the change in electrical potential energy in moving a positive 4 nC charge from A to B, where A is 3 cm from the source charge and B is 10 cm away. c. Determine the change in electrical potential energy in moving a negative 4 nC charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential U elec = qV; V = U elec / q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. <= Replace before using Slide 21-10 Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge V= PEe !! qtest !V = !PEe W =" e qtest qtest Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where Delta V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and Delta PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential and E-Field for Three Important Cases For a point charge q 1 q V=K = r 4!" 0 r For very large charged plates, must use ! ! ! ! ! ! ! !PEe We Fe !i!!r qtest E!i!!r ! !V = =" =" =" = " E!i!!r = " E !r cos # qtest qtest qtest qtest Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-14 Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-14 Example A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-15 Chapter 22 Current and Resistance Topics: • Current • Conservation of current • Batteries • Resistance and resistivity • Simple circuits Sample question: How can the measurement of an electric current passed through a person s body allow a determination of the percentage body fat? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-1 Properties of a Current Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-8 Brainstorm: what is used up when current flows? (Penguin Racetrack Demo) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 Definition of a Current The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-9 Simple Circuits The current is determined by the potential difference and the resistance of the wire: ∆V _____ chem I = R Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-13 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-3 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-4 Batteries The potential difference between the terminals of a battery, often called the terminal voltage, is the battery s emf. Wchem !Vbat = =e q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-20 Series and Parallel Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-1 Resistivity The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The resistance of a wire depends on its dimensions and the resistivity of its material: The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-22 Kirchhoff s Laws Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 23-11 The V field • Can we describe electric fields using the concepts of work and energy? • To do so, we need to describe the electric field not as a force-related E field, but as an energy-related field. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential due to a single charged object Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Finding the electric potential energy when the V field is known • If we know the electric potential at a specific location, we can rearrange the definition of the V field to determine the electric potential energy: Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The superposition principle and the V field due to multiple charges • where Q , Q , Q , … are the source charges 1 2 3 (including their signs) creating the field and r1, r2, r3, … are the distances between the source charges and the location where we are determining the V field. • So Electric Potentials (V) add just like Electric Potential Energies Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Quantitative Example • Suppose that the heart's dipole charges −Q and +Q are separated by distance d. Write an expression for the V field due to both charges at point A, a distance d to the right of the +Q charge. 1. Simplify and diagram. 2. Represent mathematically. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Finding the electric potential energy when the V field is known • If we know the electric potential at a specific location, we can rearrange the definition of the V field to determine the electric potential energy: Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Potential difference – Delta V • The value of the electric potential depends on the choice of zero level, so we often use the difference in electric potential between two points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Particles in a potential difference • A positively charged object accelerates from regions of higher electric potential toward regions of lower potential (like an object falling to lower elevation in Earth's gravitational field). • A negatively charged particle tends to do the opposite, accelerating from regions of lower potential toward regions of higher potential. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

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