Fields: Gravitational and Electric field

1 P01 -Physics 8.02TFor now, please sit anywhere, 9 to a table2 P01 -Class 1: OutlineHour 1:Why Physics?Why Studio Physics? (& How?)Vector and Scalar FieldsHour 2:Gravitational fieldsElectric fields3 P01 -Why Physics?4 P01 -Why Study Physics?Understand/appreciate nature•Lightning•Soap Films•Butterfly Wings•Sunsets5 P01 -Why Study Physics?Electromagnetic phenomena led directly to Einstein’s discovery of the nature of space and time, see his paper ON THE ELECTRODYNAMICSOF MOVING BODIESA. Einstein June 30, 1905In the last class of the term before the review, we will explain to you how this comes about6 P01 -Why Study Physics?•Understand/Appreciate Nature•Understand Technology§Electric Guitar§Ground Fault Interrupts§Microwave Ovens§Radio Towers7 P01 -Why Study Physics?•Understand/Appreciate Nature•Understand Technology•Learn to Solve Difficult Problems•It’s Required8 P01 -Why Studio Physics?9 P01 -Why The TEAL/Studio Format?Problems with Large Lectures:Lecture/recitations are passiveNo labs 􀃆lack of physical intuition E&M is abstract, hard to visualizeTEAL/Studio Addresses Problems:Lectures 􀃆Interactive, Collaborative LearningIncorporates desk top experimentsIncorporates visualization/simulationsBottom Line: Learn More, Retain More, Do Better10 P01 -Why The TEAL/Studio Format?By standard assessment measures, TEAL shows a factor of two increase in learning gains as compared to lecture/recitation format(see Doriand Belcher, “How Does TEAL Affect Student Learning of E&M Concepts?”, Journal of the Learning Sciences14(2) 2004.) Bottom Line: Learn More, Retain More, Do Better11 P01 -Overview of TEAL/StudioCollaborative LearningGroups of 3, Tables of 9You teach, you discuss, you learnIn-Class Problem SolvingDesktop ExperimentsTeacher-Student InteractionVisualizationsPRS Questions12 P01 -Personal Response System(PRS) Question:Physics ExperiencePick up the nearest PRS(under the table in a holder)13 P01 -Your ResponsibilitiesBefore Class: Read SummaryIn Class: (You must be present for credit)Problem Solving, Desktop Experiments, PRSAfter Class:Read Study Guide, Review VisualizationsHomework (Tuesdays 4:15 pm)Exams3 Midterms (45%) + Final (25%)14 P01 -To Encourage Collaboration, Grades Are NOT Curved In 8.02:+-A>=95<95 & >=90<90 & >=85B<85 & >=80<80 & >=75<75 & >=70C<70 & >=67<67 & >=64<64 & >=60D<60 & >=55 F<5515 P01 -Honesty IssuesProblem Sets: Please work together BUT Submit your own, uncopied workIn Class Assignments:Must sign your own name to submitted workSigning another’s name is COD offensePRS:Use only your assigned PRSUsing another’s PRS is COD offense16 P01 -Physics 8.02 StaffIncludes:LecturerDemo Group Graduate TAUGrad TAs17 P01 -TextbooksRequired:“Introduction to E & M”Liao, Dourmashkin, and BelcherSupplemental (not required):Serway& Jewett 6thEdition; Giancoli; …Prefer something else? Let me know!Important: Find something you can read18 P01 -Common Questions & Answers•Dysfunctional Group?•Must Miss Class?•Must Miss HW?•Must Miss Exam?•Tell Grad TA•Tell Grad TA•Tell Grad TA•Tell me ASAPExam dates & times are onlineDo NOT schedule early vacation departures, etc. without consulting these times!Any Questions?19 P01 -Physics is not Math…20 P01 -…but we use concepts from 18.02V=−∇E􀁇•Gradients•Path Integrals•Surface Integrals•Volume IntegralsBAVd∆≡−⋅∫Es􀁇􀁇0inSQdε⋅=∫∫EA􀁇􀁇􀁷QdVρ=∫∫∫21 P01 -PRS Question:Math Background22 P01 -Don’t Worry!•For many this is new & I will introduce concepts before use (yell at me if not!)•Concepts are VERY important –mechanics are almost trivialMath introduction/review:A time will be scheduledPresentation slides will be posted23 P01 -So what physics do we learn in 8.02 anyway????24 P01 -What’s the Physics?8.01: Intro. to basic physics concepts: motion, force, energy, …How does matter interact?Four Fundamental Forces:Long range: Gravity (8.01 … Gen.Relativity)Short Range: Strong and WeakMid Range: Electromagnetic (8.02)25 P01 -8.02: Electricity and MagnetismAlso new way of thinking…How do objects interact at a distance? FieldsWe will learn about E & M Fields: how they are created & what they effectBig Picture Summary:00000inBSCEencSCQddddtdddIdtεµµεΦ⋅=⋅=−Φ⋅=⋅=+∫∫∫∫∫∫EAEsBABs􀁇􀁇􀁇􀁇􀁇􀁇􀁇􀁇􀁷􀁶􀁷􀁶MaxwellEquations:()q=+×FEvB􀁇􀁇􀁇􀁇LorentzForce:26 P01 -Today: FieldsIn General, thenGravitational & Electric27 P01 -Scalar Fieldse.g. Temperature: Every location has associated value (number with units)28 P01 -Scalar Fields -Contours•Colors represent surface temperature•Contour lines show constant temperatures29 P01 -Fields are 3D•T = T(x,y,z)•Hard to visualize 􀃆Work in 2D30 P01 -Vector FieldsVector (magnitude, direction) at every point in spaceExample: Wind Velocity Vector Field31 P01 -Vector Field ExamplesBegin with Fluid Flow32 P01 -Vector Field ExamplesFlows With Sources(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/vectorfields/02-particleSource/02-ParticleSource_320.html)33 P01 -Vector Field ExamplesFlows With Sinks(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/vectorfields/01-particleSink/01-ParticleSink_320.html)34 P01 -Vector Field ExamplesCirculating Flows(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/vectorfields/03-particleCirculate/03-PartCircMotion_320.html)35 P01 -Visualizing Vector Fields:Three MethodsVector Field DiagramArrows (different colors or length) in direction of field on uniform grid.Field LinesLines tangent to field at every point along lineGrass SeedsTextures with streaks parallel to field directionAll methods illustrated inhttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/39-pcharges/39-twocharges320.html36 P01 -Vector Fields –Field Lines•Direction of field line at any point is tangent to field at that point•Field lines never cross each other37 P01 -PRS Question:Vector FieldIn General: Don’t pick up unit until ready to answerThen I’ll know when class is ready38 P01 -Vector Fields –“Grass Seeds”Source/SinkCirculatingAlthough we don’t know absolute direction, we can determine relative direction39 P01 -PRS Questions:“Grass Seed” Visualizations40 P01 -Weird Field ContestPurposeGain familiarity with vector fieldsWinnerDisplayed in MIT Museum ExhibitDue DateTurn in with 2ndPSet in Separate Box41 P01 -Another Vector Field:Gravitational Field42 P01 -2ˆgMmGr=−Fr􀁇Example Of Vector Field: GravitationGravitational Force:Gravitational Field:22/ˆˆgGMmrMGmmr==−=−Fgrr􀁇􀁇M: Mass of Earth43 P01 -Example Of Vector Field: GravitationGravitational Field:2ˆMGr=−gr􀁇gm=Fg􀁇􀁇Createdby MFeltby mˆ:runit vector from Mto mrrr􀁇=ˆM: Mass of Earth3MGr⇒=−gr􀁇􀁇44 P01 -In Class ProblemFind the gravitational field at point PBonus: Where would you put another mass m to make the field become 0 at P?g􀁇g􀁇NOTE: Solutions will be posted within one day of class45 P01 -From Gravitational toElectric Fields46 P01 -Electric Charge (~Mass)Two types of electric charge: positive and negativeUnit of charge is the coulomb[C] Charge of electron (negative) or proton (positive)isCharge is quantizedCharge is conserved19,1.60210eeC−±=×QNe=±npeν−→++eeγγ+−+→+47 P01 -Electric Force (~Gravity)The electric force between charges q1and q2is(a)repulsive if charges havesame signs (b)attractive if charges haveopposite signs Like charges repel and opposites attract !!48 P01 -Coulomb's Law12122ˆeqqkr=Fr􀁇Coulomb’s Law: Force by q1on q2922018.987510 N m/C4ekπε==׈:runit vector from q1to q2rrr􀁇=ˆ12123eqqkr⇒=Fr􀁇􀁇49 P01 -Coulomb's Law: Example()313222ˆˆm1mr=−=rij􀁇?32=F􀁇a = 1 mq1= 6 Cq3= 3 Cq2= 3 C32r􀁇()()()()()129223ˆˆ3m910NmC3C3C1m−=×ij32323ekqqr=rF􀁇􀁇()98110ˆˆ3N2×=−ij50 P01 -The Superposition PrincipleMany Charges Present:Net force on any charge is vector sum of forces from other individual charges31323=+FFF􀁇􀁇􀁇Example:In general:1Njiji==∑FF􀁇􀁇51 P01 -Electric Field(~g)The electric field at a point is the force acting on a test charge q0at that point, divided by the charge q0:0q≡FE􀁇􀁇2ˆeqkr=Er􀁇For a point charge q:http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/04-MovingChargePosElec/04-MovChrgPosElec_f223_320.html52 P01 -Superposition PrincipleThe electric field due to a collection of Npoint charges is the vector sum of the individual electric fields due to each charge121.....Ntotalii==++=∑EEEE􀁇􀁇􀁇􀁇53 P01 -Summary Thus FarMass MCharge q(±)2ˆMGr=−gr􀁇2ˆeqkr=Er􀁇CREATE:gm=Fg􀁇􀁇Eq=FE􀁇􀁇This is easiest way to picture fieldFEEL:54 P01 -PRS Question:Electric Field