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Chapter 21 Electric Potential Topics: • Electric potential energy • Electric potential • Conservation of energy • Equipotential • Contour Maps • Capacitance 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 Electricity key concepts (Chs. 20 & 21) - Slide 1 General Concepts - These are always true Electric Force and Field Model • Charge Model • E-field • Definition • E-field vectors Fe, s®t E= qt • E-field lines å Þ Fe, s®t = qE Ex = E1x + E2 x + E3x + ××× • Superposition E = (note that for forces and fields, we need to work in vector components) net x Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity key concepts (Chs. 20 & 21) - Slide 2 General Concepts - These are always true Energy, Electric Potential Energy, and Electric Potential • Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V • Conservation of Energy • Work by Conservative force = -- change of PE • Electric Potential Energy and Electric Potential Energy PEe Ve = qt Þ Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. PEe = qVe Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Work done by a conservative force (Fg, Fs, & Fe) Also work done by conservative force Wg = -DPEg is path independent q1q2 PEe = k r12 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 PEe V= qtest DPEe We DV = =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 elta V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and elta PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 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) Elta Potential Energy for a uniform infinite plate DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a 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 PEe V= qtest DPEe We DV = =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 elta V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and elta PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential and E-Field for Three Important Cases For a point charge q 1 q V=K = r 4pe 0 r For very large charged plates, must use Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 E-field lines and Equipotential lines 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 V • 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. Slide 21-16 Connecting Potential and Field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-31 Reading Quiz 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-12 Answer 4. The electric field A. B. C. D. is always perpendicular to an equipotential surface. is always tangent to an equipotential surface. always bisects an equipotential surface. makes an angle to an equipotential surface that depends on the amount of charge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 Example Problem Source charges create the electric potential shown. 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? 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-33 Graphical Representations of Electric Potential Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-13 The Potential Inside a Parallel-Plate Capacitor Uelec Q V= = Ex = x q Î0 A Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Electric Potential of a Point Charge Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-27 Discussion of other units for Energy and E-field 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 10-19 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. Slide 21-16 Batteries The potential difference between the terminals of a battery, often called the terminal voltage, is the battery’s emf. W chem ∆Vbat = ____ =e q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 22-12 Parallel Plate Capacitor 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. Slide 21-16 Parallel Plate Capacitor (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. Slide 21-16 Define Capacitance 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. Slide 21-16 The Capacitance of a Parallel-Plate Capacitor e0 A C= d Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-31 Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔVC between the electrodes: Q = C DVC Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-29 Charging a Capacitor Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-30 Capacitors 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. Slide 21-16 Energy stored in Capacitor – Storing Energy in E-field 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. Slide 21-16 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: = ke 0 Dielectric strength is the maximum field a dielectric can experience without breaking down. E0 E'= k 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) Capacitance • C = |Q| / |Delta V| • Property of the conductors and the dielectric Special Case - Parallel Plate Capacitor • C = Kappa * Epsilon0*A / d Energy • Pee = 1/2 |Q| |Delta V| • |Delta V| = Ed Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16