Lecture 2 Lecture 2 --CoulombCoulomb’’s Law and Electric Fields Law and Electric FieldChapters 25 and 26 Chapters 25 and 26 --Thursday January 11thThursday January 11th•Quick review of Tuesday’s class•Coulomb’s Law•Scalar and vector notation•Discrete charge distributions (superposition principle)•Continuous charge distributions•Electric fields•Discrete charge distributions•Continuous charge distributions•Electric field linesReading: pages 567 thru 597 (chapters 25 & 26) in HRKReading: pages 567 thru 597 (chapters 25 & 26) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssign: set 1, due Thur. 18th at 11:59pmWebAssign: 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. 7, 14, 23 ; Prob. 1Ex. 7, 14, 23 ; Prob. 1What is charge?What is charge?•Charge is measured in Coulomb’s (C)•Fundamental unit.•Definition based on forces between current carrying wires (current = Ampères, or C/s), i.e. chapter 33.•Charge is discrete•Thompson discovered the electron in 1896. He found that charge was carried by elementary particles with the same charge to mass ratio.•The elementary charge of the electron was not measured until 1909 (Millikan).•Both experiments earned Nobel prizes.Charge on an electron: e = 1.6 × 10−19Coulombs1 Coulomb of charge: 6.24 × 1018electrons1 Ampère (= 1 C/s) 6.24 × 1018electrons/secondCharge is discrete: q = ne n = ±1, ±2, ±3,...Static electricity through chargingStatic electricity through chargingConductorConductorInsulatorInsulatorCoulombCoulomb’’s Law s Law CoulombCoulomb’’s s torsionaltorsionalbalancebalance178512 1222,or qq qqFFKrr∝=92218.99 10 N m /C4oKπε==×⋅εο= 8.85418781762 × 10-12C2/N·m2()72221410Ns/Cocεπ−=×⋅×c = speed of light in vacuum= 299792458 m/s1212 12 212121221 212211ˆ41ˆ4ooqqrqqrπεπε==−=FrFFrGGG1212 2112ˆˆr==−rrrGCoulombCoulomb’’s Law in vector notation s Law in vector notationSuperposition principleSuperposition principleTest chargeSourcecharges0123...qiii=+++ =∑FFFF F FGGGG G G•Leads to Maxwell’s equations being linear.Calculus (continuous charge distribution):Calculus (continuous charge distribution):ˆˆˆxyzdidFjdF k dF== + +∫∫ ∫ ∫FFGG021ˆ4oqdqdrπε=FrGq0= test chargeq0Charge 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 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 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
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