Lecture 3 Lecture 3 --Electric FieldElectric FieldChapter 26 Chapter 26 --Tuesday January 16thTuesday January 16th•Electric fields•Discrete charge distributions•Continuous charge distributions•Electric field lines•Motion of charges in electric fields•Point charges•Dipoles•Determination of the fundamental unit of chargeReading: pages 587 thru 603 (chapter 26) in HRKReading: pages 587 thru 603 (chapter 26) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssignWebAssignHwkHwk: set 1, due Thur. 18th at 11:59pm: set 1, due Thur. 18th at 11:59pmGraded problems: Ch. 26 Graded problems: Ch. 26 ––Ex. 8, 13, 18, 36; Prob. 10Ex. 8, 13, 18, 36; Prob. 10Practice problems: Ch. 26 Practice problems: Ch. 26 --Ex. 27, 35, 37; Prob. 11,15Ex. 27, 35, 37; Prob. 11,15Electric field Electric field --Chapter 26Chapter 26Analogy with gravitationAnalogy with gravitation••Problem:Problem:Force depends on test massForce depends on test mass!!2ˆGMmr=−FrGormm==FFg gGGGG••But:But:2ˆGMr=−grG••Same for all masses.Same for all masses.••Represents the gravitational Represents the gravitational influence (field) of the mass influence (field) of the mass MM. . m02ˆqqKr=FrGElectric field Electric field --Chapter 26Chapter 26Analogy with gravitationAnalogy with gravitation++q0••Problem:Problem:Force depends on test chargeForce depends on test charge!!00orqq==FFE EGGG G••Definition:Definition:21ˆ4oqrπε=ErG••Same for all test charges.Same for all test charges.••Represents the electrostatic Represents the electrostatic influence (field) of the charge influence (field) of the charge qq. . q = −Qsource chargeElectric field Electric field --Chapter 26Chapter 260q=FEGGNewton’s law for electrostatics:There’s really no need for the “test charge”q=FEGGThis is the force on a charge q in an electric fieldEGUnits for Units for EEare N/C in this chapter are N/C in this chapter (later we shall use volts per meter)(later we shall use volts per meter)Electric field Electric field --Chapter 26Chapter 2621ˆ4oqrπε=ErGCoulomb’s law:•Note that the force may be directed both towards and away from the source charge, since this charge may be either positive or negative.•Length of arrow signifies magnitude of EG123...iii=+++ =∑EE E E E EGG G G G GˆˆˆxyzdidEjdE k dE== + +∫∫ ∫ ∫EEGGOf course, superposition principle still holds:Electric field Electric field --Chapter 26Chapter 26Units for Units for EEare N/C in this chapter are N/C in this chapter (later we shall use volts per meter)(later we shall use volts per meter)(V/m)(V/m)Charge densitiesCharge densitiesIn 1D (a line or wire):In 1D (a line or wire):,orQdQLdLλλ==λis the line charge density, or charge per unit length, in Coulombs per meter. L represents length, and Q is charge.In 2D (a surface or sheet):In 2D (a surface or sheet):,orQdQAdAσσ==σis the surface charge density, or charge per unit area in Coulombs per meter2; A represents area, and Q is charge.In 3D (a solid object):In 3D (a solid object):,orQdQVdVρρ==ρis the volume charge density, or charge per unit volume in Coulombs per meter3. V represents volume, and Q is charge.Electric field linesElectric field lines• The tangent to an electric field line at a point in space gives the direction of the electric field at that point.• The magnitude of the electric field at any point is proportional to the number of field lines per unit cross-sectional area perpendicular to the lines.• Electric field lines start on positive charges and end on negative charges (can also start/end at infinity). • The symmetry of the problem dictates the directions in which field lines radiate from charges.Electric field linesElectric field lines• The number of field lines radiating from a charge is proportional to the charge.Electric field linesElectric field linesThe Electric DipoleThe Electric DipoleDipole moment:pqd or q==pdGGOn the median plane (along x axis):()314zopExdxπε=−>>On the dipole axis (along z axis):()312zopEzdzπε=>>Motion of charges in electric fieldsMotion of charges in electric fieldsqm==FE aGGGqm⇒=aEGGMotion of charges in electric fieldsMotion of charges in electric fieldsqm==FE aGGGqm⇒=aEGGProjectile motion (PHY 2060 or 2048)2100 00200yxyy xxyy vt at xx vtvv at vv−= + −==+ =A Dipole in an Electric FieldA Dipole in an Electric FieldsinsinsinFdqdEpEτθθθ====×pEGGcosUpEθ=−=− ⋅pEGGForceForce= = gradient in the potential energygradient in the potential energyDiscovery of the electron: J. J. Thompson's experimentDiscovery of the electron: J. J. Thompson's experimentCathode ray tube Cathode ray tube --or CRTor CRTBasis for so much technology: TV, oscilloscope, mass spectrometeBasis for so much technology: TV, oscilloscope, mass spectrometer, etc...r, etc...Charged particles Charged particles evaporate from evaporate from heated cathode C. heated cathode C. Negative charges Negative charges accelerate in electric accelerate in electric field between the field between the cathode and anode A.cathode and anode A.Electric field betweenElectric field betweenD and E used to deflect beam.D and E used to deflect beam.Well focused beam of Well focused beam of negative particles passes negative particles passes through the slit B.through the slit B.Phosphorescent Phosphorescent screen used to screen used to detect the cathode detect the cathode ray.ray.Thompson also applied a Thompson also applied a magnetic field into the page, magnetic field into the page, which also deflected the ray.which also deflected the ray.In order to measure q/m it is essential to know the velocity of the beam.F = qE = maqaEm⇒=The rest is simply E and MThe rest is simply E and M•vxis obtained by nulling the deflection with both electric and magnetic fields (we will discuss the magnetic part in later chapters).•Thompson then switched off the magnetic field, and measured the ray deflection due to the electric field between D & E.•The deflection depends on vx, the dimensions of the apparatus (x1, x2, y1and y2, etc..), and on the ratio of q/m.vxvyvxMillikan's oil drop experimentMillikan's oil drop experimenthttp://www.http://www.whfreemanwhfreeman.com/.com/modphysicsmodphysics/PDF/3/PDF/3--1bw.pdf1bw.pdfMost dropsMost dropscarry a chargecarry a chargeElectric field appliedElectric field appliedbetween capacitor platesbetween capacitor platesto provide upwards forceto provide upwards forceon some
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