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MIT 8 02T - Study Notes

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Electric ChargeCoulomb's LawAnimation 2.1: Van de Graaff GeneratorPrinciple of SuperpositionExample 2.1: Three ChargesElectric FieldAnimation 2.2: Electric Field of Point ChargesElectric Field LinesForce on a Charged Particle in an Electric FieldElectric DipoleThe Electric Field of a DipoleAnimation 2.3: Electric DipoleDipole in Electric FieldFigure 2.8.1 Electric dipole placed in a uniform field.Potential Energy of an Electric DipoleCharge DensityVolume Charge DensitySurface Charge DensityLine Charge DensityElectric Fields due to Continuous Charge DistributionsExample 2.2: Electric Field on the Axis of a RodExample 2.3: Electric Field on the Perpendicular BisectorExample 2.4: Electric Field on the Axis of a RingExample 2.5: Electric Field Due to a Uniformly Charged DiskSummaryProblem-Solving StrategiesSolved ProblemsHydrogen AtomMillikan Oil-Drop ExperimentCharge Moving Perpendicularly to an Electric FieldElectric Field of a DipoleElectric Field of an ArcElectric Field Off the Axis of a Finite RodConceptual QuestionsAdditional ProblemsThree Point ChargesThree Point ChargesFour Point ChargesSemicircular WireElectric DipoleCharged Cylindrical Shell and CylinderTwo Conducting BallsTorque on an Electric DipoleChapter 2 Coulomb’s Law 2.1 Electric Charge........................................................................................................ 2 2.2 Coulomb's Law ....................................................................................................... 2 Animation 2.1: Van de Graaff Generator.................................................................. 3 2.3 Principle of Superposition....................................................................................... 4 Example 2.1: Three Charges....................................................................................... 4 2.4 Electric Field........................................................................................................... 6 Animation 2.2: Electric Field of Point Charges ........................................................ 7 2.5 Electric Field Lines................................................................................................. 8 2.6 Force on a Charged Particle in an Electric Field .................................................... 9 2.7 Electric Dipole...................................................................................................... 10 2.7.1 The Electric Field of a Dipole......................................................................... 11 Animation 2.3: Electric Dipole................................................................................ 12 2.8 Dipole in Electric Field......................................................................................... 12 2.8.1 Potential Energy of an Electric Dipole ........................................................... 13 2.9 Charge Density...................................................................................................... 15 2.9.1 Volume Charge Density.................................................................................. 15 2.9.2 Surface Charge Density .................................................................................. 16 2.9.3 Line Charge Density ....................................................................................... 16 2.10 Electric Fields due to Continuous Charge Distributions....................................... 17 Example 2.2: Electric Field on the Axis of a Rod .................................................... 17 Example 2.3: Electric Field on the Perpendicular Bisector...................................... 18 Example 2.4: Electric Field on the Axis of a Ring................................................... 20 Example 2.5: Electric Field Due to a Uniformly Charged Disk............................... 22 2.11 Summary............................................................................................................... 24 2.12 Problem-Solving Strategies .................................................................................. 26 2.13 Solved Problems ................................................................................................... 28 2.13.1 Hydrogen Atom ........................................................................................... 28 2.13.2 Millikan Oil-Drop Experiment .................................................................... 29 2.13.3 Charge Moving Perpendicularly to an Electric Field .................................. 30 2.13.4 Electric Field of a Dipole............................................................................. 32 2.13.5 Electric Field of an Arc................................................................................ 35 2.13.6 Electric Field Off the Axis of a Finite Rod.................................................. 36 02.14 Conceptual Questions ........................................................................................... 38 2.15 Additional Problems ............................................................................................. 39 2.15.1 Three Point Charges..................................................................................... 39 2.15.2 Three Point Charges..................................................................................... 39 2.15.3 Four Point Charges ...................................................................................... 40 2.15.4 Semicircular Wire........................................................................................ 40 2.15.5 Electric Dipole ............................................................................................. 41 2.15.6 Charged Cylindrical Shell and Cylinder...................................................... 41 2.15.7 Two Conducting Balls ................................................................................. 42 2.15.8 Torque on an Electric Dipole....................................................................... 42 1Coulomb’s Law 2.1 Electric Charge There are two types of observed electric charge, which we designate as positive and negative. The convention was derived from Benjamin Franklin’s experiments. He rubbed a glass rod with silk and called the charges on the glass rod positive. He rubbed sealing wax with fur and called the charge on the sealing wax negative. Like charges repel and opposite charges attract each other.


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