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Chapter 21 Electric Potential Topics: • Electric potential energy • Electric potential • Conservation of energy • Capacitors and 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. The Capacitance of a Parallel-Plate Capacitor e0 A C= d Slide 21-31 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 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 Dielectrics and Capacitors 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. 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 A C= d Dielectric strength is the maximum field a dielectric can experience without breaking down. E' = E0 k Energy stored in Capacitor – Storing Energy in E-field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Energy Model Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Capacitance Model Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 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! 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 Properties of a Current Slide 22-8 Light the Bulb Can you light a bulb when you have • 1 battery • 1 Bulb • 1 wire • A - yes • B - no Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Definition of a Current Slide 22-9 Storage of Electric Energy Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives. The Electrocardiogram (ECG or EKG) The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart. Capacitors Note: Battery is a source of constant potential What happens when you insert a dielectric? • 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 • Energy stored Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 • E-field lines r Fe, st E qt r r Fe, st qE Exnet Ex E1x E2 x E3x • 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 General Concepts - These are always true Energy, Electric Potential Energy, and Electric Potential • Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V • Work-Energy Theorem • Conservation of Energy • Work by Conservative force = -- change of PE • Electric Potential Energy and Electric Potential Energy PEe Ve qt Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. PEe qVe Electricity - concepts (Chs 20 & 21) General Concepts - These are always true Electric Force and Field Model • Charge Model • E-field • Definition r Fe, st E qt r r Fe, st qE • E-field vectors • E-field lines • Superposition Exnet E1x E2 x E3x Energy, Electric Potential Energy, and Electric Potential • Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V • Work-Energy Theorem • Conservation of Energy Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electricity - General key concepts (Chs 20 & 21) Charge Model • Electric forces can be attractive or repulsive • Objects with the same sign of charge repel each other • Objects with the opposite sign of charge attract each other • Neutral objects are polarized by charged objects which creates attractive forces between them • There are two kinds of charges, positive (protons) and negative (electrons). In solids, electrons are charge carriers (protons are 2000 time more massive). • A charged object has a deficit of electrons (+) or a surplus of electrons (-). Neutral objects have equal numbers of + and – charges • Fe gets weaker with distance: Fe α 1/r2 • Fe between charged tapes are > Fe between charged tapes & neutral objects • Rubbing causes some objects to be charged by charge separation • Charge can be transferred by contact, conduction, and induction • Visualization => charge diagrams Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Nature of Electric Field Vectors • Test charge is a small positive charge to sample the E-Field • Charge of test charge is small compared to source charges (source charges are the charges that generate the field) • E-field vectors • E-field is the force per charge E = Fe / q • E-field vectors points away from + charges • E-field vectors point towards - charges • E-field for point charges gets weaker as distance from source point charges increases • For a point charge E = Fe / q = [k Q q / r2] / q = k Q / r2 • Electric Force Fe = qE Nature of Electric Field Lines • E-Field lines start on + charges and end on -- charges • Larger charges will have more field lines going out/coming in • Density of Field lines is a measure of field strength – the higher the density the stronger the field • The E-field vector at a point in space is tangent to the field line at that point. If there is no field line, extrapolate Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work r r r r Work W F g 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. different types PE f Eth 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) Potential Energy for a uniform infinite plate r r 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 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 PEe We V 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 V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and PEe= 0 J) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.