Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy Electric potential Conservation of energy Equipotential Contour Maps Capacitance Chapter 21 Electric Potential Topics: 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? Slide 21-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity key concepts (Chs. 20 & 21) - Slide 1 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. General Concepts - These are always true Electric Force and Field Model Charge Model E-field Definition E-field vectors E-field lines Superposition (note that for forces and fields, we need to work in vector components)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity key concepts (Chs. 20 & 21) - Slide 2 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. General Concepts - These are always true Energy, Electric Potential Energy, and Electric Potential Energy Definitions: KE, PE e, Pe g, W, E sys, E th and V Conservation of Energy Work by Conservative force = -- change of PE Electric Potential Energy and Electric Potential Energy

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart)  elta Potential Energy for a uniform infinite plate For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or in between the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge 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  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  PE e = 0 J) Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart)  Elta Potential Energy for a uniform infinite plate For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or in between the two plates Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Potential Energy per Charge 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  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  PE e = 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Electric Potential and E-Field for Three Important Cases Slide For a point charge For very large charged plates, must use

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field lines and Equipotential lines Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field Lines Go from + charges to - charges Perpendicular at surface of conductor or charged surface E-field in stronger where E-field lines are closer together More charge means more lines Equipotential Lines Parallel to conducting surface Perpendicular to E-field lines Near a charged object, that charges influence is greater, then blends as you to from one to the other E-field is stronger where Equipotential lines are closer together Spacing represents intervals of constant ΔV Higher potential as you approach a positive charge; lower potential as you approach a negative charge

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Connecting Potential and Field Slide 21-31

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Reading Quiz 4.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. Slide 21-12

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer 4.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. Slide 21-13

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude? B.Is the magnitude of the electric field at A greater than, equal to, or less than at point D? Example Problem Source charges create the electric potential shown. C.What is the approximate magnitude of the electric field at point C? D.What is the approximate direction of the electric field at point C? Slide 21-33

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Graphical Representations of Electric Potential Slide 21-13

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Potential Inside a Parallel-Plate Capacitor Slide 21-25

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential of a Point Charge Slide 21-27

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Discussion of other units for Energy and E-field Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. eV – electron Volts => Unit of energy for particle accelerators The energy gained by an electron that goes through a potential difference of one volt 1 eV = 1.60 x J V/m – Volts per meter => Unit of Electric Field |Delta V| = |E||Delta r| => |E| = |Delta V| / |Delta r| [E] = V / m

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Batteries The potential difference between the terminals of a battery, often called the terminal voltage, is the battery’s emf. Slide ∆ V bat = =  W chem q ____

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Parallel Plate Capacitor Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Parallel Plate Capacitor Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. (a) Parallel-plate capacitor connected to battery. (b) Battery and Capacitor in a circuit diagram. Relationship of E-field & Delta V? Delta V

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Define Capacitance Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance is a measure of how much charge can be stored in a capacitor for a given amount of voltage

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Capacitance of a Parallel-Plate Capacitor Slide 21-31

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔV C between the electrodes: Slide 21-29

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charging a Capacitor Slide 21-30

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Note: Battery is a source of constant potential What happens when you pull the plates of a capacitor apart? With a Battery connected With no Battery connected Do the following quantities (a) increase, (b) decrease, or (c) remain the same: Charge E-Field Delta V

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy stored in Capacitor – Storing Energy in E-field Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectrics and Capacitors

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectrics and Capacitors The molecules in a dielectric tend to become oriented in a way that reduces the external field. This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectric Constant With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ: Dielectric strength is the maximum field a dielectric can experience without breaking down.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Storage of Electric Energy The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field: (17-11) The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors and Capacitance (Key Equations) Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance C = |Q| / |Delta V| Property of the conductors and the dielectric Special Case - Parallel Plate Capacitor C = Kappa * Epsilon 0 *A / d Energy Pe e = 1/2 |Q| |Delta V| |Delta V| = Ed