Chapter 23 Lecture - Uml.edu

PHYSICSFOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH4/EChapter 23 LectureRANDALL D. KNIGHT 2017 Pearson Education, Inc.

Chapter 23 The Electric FieldIN THIS CHAPTER, you will learn how tocalculate and use the electric field. 2017 Pearson Education, Inc.Slide 23-2

Chapter 23 Preview 2017 Pearson Education, Inc.Slide 23-3

Chapter 23 Preview 2017 Pearson Education, Inc.Slide 23-4

Chapter 23 Preview 2017 Pearson Education, Inc.Slide 23-5

Chapter 23 Preview 2017 Pearson Education, Inc.Slide 23-6

Chapter 23 Preview 2017 Pearson Education, Inc.Slide 23-7

Chapter 23 Content, Examples, andQuickCheck Questions 2017 Pearson Education, Inc.Slide 23-8

Four Key Electric Fields: Slide 1 of 2 2017 Pearson Education, Inc.Slide 23-9

Four Key Electric Fields: Slide 2 of 2 2017 Pearson Education, Inc.Slide 23-10

Electric Field of a Point Charge 2017 Pearson Education, Inc.Slide 23-11

The Electric Field The electric fieldwas defined as on q/qwhere on q is theelectric force ontest charge q. The SI units ofelectric field arethereforeNewtons perCoulomb (N/C). 2017 Pearson Education, Inc.Slide 23-12

The Electric Field of Multiple Point Charges Suppose the source of an electric field is a group ofpoint charges q1, q2, The net electric field Enet is the vector sum of theelectric fields due to each charge. In other words, electric fields obey the principle ofsuperposition. 2017 Pearson Education, Inc.Slide 23-13

Problem-Solving Strategy: The Electric Field ofMultiple Point Charges 2017 Pearson Education, Inc.Slide 23-14

Problem-Solving Strategy: The Electric Field ofMultiple Point Charges 2017 Pearson Education, Inc.Slide 23-15

Electric Dipoles Two equal butopposite chargesseparated by asmall distance forman electric dipole. The figure showstwo examples. 2017 Pearson Education, Inc.Slide 23-16

The Dipole Moment It is useful to define thedipole moment p,shown in the figure, asthe vector: The SI units of the dipole moment are C m. 2017 Pearson Education, Inc.Slide 23-17

The Dipole Electric Field at Two Points 2017 Pearson Education, Inc.Slide 23-18

The Electric Field of a Dipole The electric field at a point on the axis of a dipole iswhere r is the distance measured from the center ofthe dipole. The electric field in the plane that bisects and isperpendicular to the dipole is This field is opposite to the dipole direction, and it isonly half the strength of the on-axis field at the samedistance. 2017 Pearson Education, Inc.Slide 23-19

Example 23.2 The Electric Field of a WaterMolecule 2017 Pearson Education, Inc.Slide 23-20

Electric Field Lines Electric field lines arecontinuous curvestangent to theelectric field vectors. Closely spaced fieldlines indicate agreater field strength. Electric field linesstart on positivecharges and end onnegative charges. Electric field linesnever cross. 2017 Pearson Education, Inc.Slide 23-21

Electric Field Lines of a Point Charge 2017 Pearson Education, Inc.Slide 23-22

The Electric Field of a Dipole This figure represents the electric field of a dipole usingelectric field lines. 2017 Pearson Education, Inc.Slide 23-23

Continuous Charge Distributions The linear chargedensity of an objectof length L andcharge Q is definedas Linear chargedensity, which hasunits of C/m, is theamount of chargeper meter of length. 2017 Pearson Education, Inc.Slide 23-24

Continuous Charge Distributions The surface charge densityof a two-dimensionaldistribution of chargeacross a surface of area Ais defined as Surface chargedensity, with unitsC/m2, is the amountof charge per squaremeter. 2017 Pearson Education, Inc.Slide 23-25

Problem-Solving Strategy: The Electric Field ofa Continuous Distribution of Charge 2017 Pearson Education, Inc.Slide 23-26

Problem-Solving Strategy: The Electric Field ofa Continuous Distribution of Charge 2017 Pearson Education, Inc.Slide 23-27

The Electric Field of a Line of ChargeThe Electric Field of a Finite Line of Example 23.3 in the textChargeuses integration to findthe electric field strengthat a radial distance r inthe plane that bisects arod of length L with totalcharge Q: 2017 Pearson Education, Inc.Slide 23-28

An Infinite Line of Charge The electric field of athin, uniformly chargedrod may be written If we now let L ,the last term becomessimply 1 and we’re leftwith 2017 Pearson Education, Inc.Slide 23-29

A Ring of Charge Consider the on-axiselectric field of a positivelycharged ring of radius R. Define the z-axis to be theaxis of the ring. The electric field on thez-axis points away fromthe center of the ring,increasing in strength untilreaching a maximumwhen z R, thendecreasing: 2017 Pearson Education, Inc.Slide 23-30

A Disk of Charge Consider the on-axiselectric field of a positivelycharged disk of radius R. Define the z-axis to be theaxis of the disk. The electric field on thez-axis points away fromthe center of the disk, withmagnitude: 2017 Pearson Education, Inc.Slide 23-31

Example 23.5 The Electric Field of a ChargedDisk 2017 Pearson Education, Inc.Slide 23-32

Example 23.5 The Electric Field of a ChargedDisk 2017 Pearson Education, Inc.Slide 23-33

A Plane of Charge The electric field of a plane of charge is found from theon-axis field of a charged disk by letting the radiusR . The electric field of an infinite plane of charge with surfacecharge density η is For a positively charged plane, with η 0, the electricfield points away from the plane on both sides of theplane. For a negatively charged plane, with η 0, the electricfield points toward the plane on both sides of the plane. 2017 Pearson Education, Inc.Slide 23-34

A Plane of Charge 2017 Pearson Education, Inc.Slide 23-35

A Sphere of Charge A sphere of charge Q and radius R, be it a uniformlycharged sphere or just a spherical shell, has anelectric field outside the sphere that is exactly thesame as that of a point charge Q located at the centerof the sphere: 2017 Pearson Education, Inc.Slide 23-36

The Parallel-Plate Capacitor The figure shows twoelectrodes, one withcharge Q and the otherwith –Q placed face-toface a distance d apart. This arrangement of twoelectrodes, chargedequally but oppositely, iscalled a parallel-platecapacitor. Capacitors play importantroles in many electriccircuits. 2017 Pearson Education, Inc.Slide 23-37

The Parallel-Plate Capacitor The figure shows twocapacitor plates, seenfrom the side. Because oppositecharges attract, all ofthe charge is on theinner surfaces of thetwo plates. Inside the capacitor,the net field pointstoward the negativeplate. Outside the capacitor,the net field is zero. 2017 Pearson Education, Inc.Slide 23-38

The Parallel-Plate Capacitor The electric field of a capacitor iswhere A is the surface area of each electrode. Outside the capacitor plates, where E and E– haveequal magnitudes but opposite directions, the electricfield is zero. 2017 Pearson Education, Inc.Slide 23-39

The Ideal Capacitor The figure shows theelectric field of anideal parallel-platecapacitor constructedfrom two infinitecharged planes. The ideal capacitor isa good approximationas long as theelectrode separation dis much smaller thanthe electrodes’ size. 2017 Pearson Education, Inc.Slide 23-40

A Real Capacitor Outside a real capacitorand near its edges, theelectric field is affectedby a complicated butweak fringe field. We will keep thingssimple by alwaysassuming the plates arevery close together andusing E η/ 0 for themagnitude of the fieldinside a parallel-platecapacitor. 2017 Pearson Education, Inc.Slide 23-41

Example 23.6 The Electric Field Inside aCapacitor 2017 Pearson Education, Inc.Slide 23-42

Example 23.6 The Electric Field Inside aCapacitor 2017 Pearson Education, Inc.Slide 23-43

Example 23.6 The Electric Field Inside aCapacitor 2017 Pearson Education, Inc.Slide 23-44

Uniform Electric Fields The figure shows anelectric field that is thesame—in strength anddirection—at everypoint in a region ofspace. This is called auniform electric field. The easiest way toproduce a uniformelectric field is with aparallel-platecapacitor. 2017 Pearson Education, Inc.Slide 23-45

Motion of a Charged Particle in an Electric Field Consider a particle of charge q and mass m at apoint where an electric field E has been producedby other charges, the source charges. The electric field exerts a force Fon q qE. 2017 Pearson Education, Inc.Slide 23-46

Motion of a Charged Particle in an Electric Field The electric field exerts a force Fon q qE on a chargedparticle. If this is the only force acting on q, it causes thecharged particle to accelerate with In a uniform field, the acceleration is constant: 2017 Pearson Education, Inc.Slide 23-47

Motion of a Charged Particle in an Electric Field “DNA fingerprints” aremeasured with thetechnique of gelelectrophoresis. A solution of negativelycharged DNA fragmentsmigrate through the gelwhen placed in a uniformelectric field. 2017 Pearson Education, Inc. Because the gel exerts adrag force, the fragmentsmove at a terminal speedinversely proportional totheir size.Slide 23-48

Dipoles in a Uniform Electric Field The figure shows anelectric dipole placed ina uniform externalelectric field. The net force on thedipole is zero. The electric field exerts atorque on the dipole thatcauses it to rotate. 2017 Pearson Education, Inc.Slide 23-49

Dipoles in a Uniform Electric Field The figure shows anelectric dipole placed ina uniform externalelectric field. The torque causes thedipole to rotate until it isaligned with the electricfield, as shown. Notice that the positiveend of the dipole is inthe direction in which Epoints. 2017 Pearson Education, Inc.Slide 23-50

Dipoles in a Uniform Electric Field The figure shows asample of permanentdipoles, such as watermolecules, in anexternal electric field. All the dipoles rotateuntil they are alignedwith the electric field. This is the mechanismby which the samplebecomes polarized. 2017 Pearson Education, Inc.Slide 23-51

The Torque on a Dipole The torque on a dipole placed in a uniform externalelectric field is 2017 Pearson Education, Inc.Slide 23-52

Example 23.9 The Angular Acceleration of aDipole Dumbbell 2017 Pearson Education, Inc.Slide 23-53

Example 23.9 The Angular Acceleration of aDipole Dumbbell 2017 Pearson Education, Inc.Slide 23-54

Example 23.9 The Angular Acceleration of aDipole Dumbbell 2017 Pearson Education, Inc.Slide 23-55

Example 23.9 The Angular Acceleration of aDipole Dumbbell 2017 Pearson Education, Inc.Slide 23-56

Example 23.9 The Angular Acceleration of aDipole Dumbbell 2017 Pearson Education, Inc.Slide 23-57

Dipoles in a Nonuniform Electric Field Suppose that a dipole isplaced in a nonuniformelectric field, such as thefield of a positive pointcharge. The first response of thedipole is to rotate until itis aligned with the field. Once the dipole is aligned, the leftward attractive forceon its negative end is slightly stronger than the rightwardrepulsive force on its positive end. This causes a net force to the left, toward the pointcharge. 2017 Pearson Education, Inc.Slide 23-58

Dipoles in a Nonuniform Electric Field A dipole near a negative point charge is alsoattracted toward the point charge. The net force on a dipole is toward the direction ofthe strongest field. Because field strength increases as you get closerto any finite-sized charged object, we canconclude that a dipole will experience a netforce toward any charged object. 2017 Pearson Education, Inc.Slide 23-59

Example 23.10 The Force on a Water Molecule 2017 Pearson Education, Inc.Slide 23-60

Example 23.10 The Force on a Water Molecule 2017 Pearson Education, Inc.Slide 23-61

Example 23.10 The Force on a Water Molecule 2017 Pearson Education, Inc.Slide 23-62

Example 23.10 The Force on a Water Molecule 2017 Pearson Education, Inc.Slide 23-63

Chapter 23 Summary Slides 2017 Pearson Education, Inc.Slide 23-64

General Principles 2017 Pearson Education, Inc.Slide 23-65

General Principles 2017 Pearson Education, Inc.Slide 23-66

Applications 2017 Pearson Education, Inc.Slide 23-67

Applications 2017 Pearson Education, Inc.Slide 23-68

The electric field of a plane of charge is found from the on-axis field of a charged disk by letting the radius R . The electric field of an infinite plane of charge with surface charge density η is For a positively charged plane, with η 0, the electric field points away from the plane on both sides of the plane.