Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy Electric potential Conservation of energy Capacitors and 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?

The Capacitance of a Parallel-Plate Capacitor Slide 21-31

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.

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

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: Dielectric strength is the maximum field a dielectric can experience without breaking down.

Energy stored in Capacitor – Storing Energy in E-field Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Energy Model Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

Capacitance Model Slide 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!

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

Properties of a Current Slide 22-8

Light the Bulb Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Can you light a bulb when you have 1 battery 1 Bulb 1 wire A - yes B - no

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

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)

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 Work-Energy Theorem Conservation of Energy Work by Conservative force = -- change of PE Electric Potential Energy and Electric Potential Energy

Electricity - concepts (Chs 20 & 21) 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 Energy, Electric Potential Energy, and Electric Potential Energy Definitions: KE, PE e, Pe g, W, E sys, E th and V Work-Energy Theorem Conservation of Energy

Electricity - General key concepts (Chs 20 & 21) Slide Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 F e gets weaker with distance: F e α 1/r 2 F e between charged tapes are > F e 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

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 = F e / 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 = F e / q = [k Q q / r 2 ] / q = k Q / r 2 Electric Force F e = 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

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 Where Work- Energy Theorem (only valid when particle model applies) Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent Conservation of Energy Equation 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)  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 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 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.