Lecture 04Physics 2049 NewsThis is WARNothing Happens! The Green thing is a Force Field!Side ViewProperties of a FORCE FIELDEXAMPLE: The Gravitational Field That We Live In.The gravitational field: gFinal Comment on Gravitational Field:Newton’s Law of GravitationThe CalculationNot quite correct ….More better …To be more precise …The Electric Field ESlide 16Electric Field Near a ChargeTwo (+) ChargesTwo Opposite ChargesA First CalculationDoing itGeneral-Continuous Charge DistributionymmetryLet’s Do it Real TimeThe mathA Harder ProblemSlide 28Completing the MathDare we project this??The GeometrySlide 32Final ResultLook at the “Field Lines”What did we learn in this chapter??What else did we learn in this chapter?Kinds of continuously distributed chargesThe SphereSummaryTo be remembered …Example:SolutionSlide 43Let’s do it backwards…EXCELSlide 46The mystery solved!!!Slide 48Slide 49Slide 50Slide 51Slide 52Week of February 17 05Electric Field 1Lecture 04The Electric FieldChapter 22 - HRWElectric Field 2Week of February 17 05Physics 2049 NewsWebAssign was due todayAnother one is posted for FridayYou should be reading chapter 22; The Electric Field.This is a very important concept.It is a little “mathy”There will be a QUIZ on Friday.Material from chapters 21-22.Studying Works!Electric Field 3Week of February 17 05This is WARYou are fighting the enemy on the planet Mongo.The evil emperor Ming’s forces are behind a strange green haze.You aim your blaster and fire … but ……Ming themercilessthis guy isMEAN!Electric Field 4Week of February 17 05Nothing Happens! The Green thing is a Force Field!The Force may not be with you ….Electric Field 5Week of February 17 05Side ViewTheFORCE FIELDForcePositiono|Force|Big!Electric Field 6Week of February 17 05Properties of a FORCE FIELDIt is a property of the position in space.There is a cause but that cause may not be known.The force on an object is usually proportional to some property of an object which is placed into the field.Electric Field 7Week of February 17 05EXAMPLE: The Gravitational Field That We Live In.mMmgMgElectric Field 8Week of February 17 05The gravitational field: gThe gravitational field strength is defined as the Force per unit mass that the field creates on an objectThis becomes g=(F/m)=(mg/m)=gThe field strength is a VECTOR.For this case, the gravitational field is constant.magnitude=g (9.8 m/s)direction= downElectric Field 9Week of February 17 05Final Comment on Gravitational Field:ggFg mmmassunitorce_Even though we know what is causing the force, we really don’t usually thinkabout it.Electric Field 10Week of February 17 05Newton’s Law of GravitationRMEarthmElectric Field 11Week of February 17 05The Calculation 226241122/77.9)104.6(1061067.6smgxxxgRMmRmMEarthEarthGFgGFElectric Field 12Week of February 17 05Not quite correct ….Earth and the Moon (in background), seen from space)Electric Field 13Week of February 17 05More better …FEarthMEarthmMoonFmoonmgElectric Field 14Week of February 17 05To be more precise …g is caused byEarth (MAJOR)moon (small)Sun (smaller yet)Mongo (extremely teeny tiny)g is therefore a function of position on the Earth and even on the time of the year or day.Electric Field 15Week of February 17 05The Electric Field EIn a SIMILAR WAYWe DEFINE the ELECTRIC FIELD STRENGTH AS BEING THE FORCE PER UNIT CHARGE.Place a charge q at a point in space.Measure (or sense) the force on the charge – FCalculate the Electric Field by dividing the Force by the charge,CoulombNewtonsqqFEEFElectric Field 16Week of February 17 05Electric Field 17Week of February 17 05Electric Field Near a ChargeElectric Field 18Week of February 17 05Two (+) ChargesElectric Field 19Week of February 17 05Two Opposite ChargesElectric Field 20Week of February 17 05A First CalculationQrqA ChargeThe spot where we wantto know the Electric FieldPlace a “test chargeat the point andmeasure the Force on it.Electric Field 21Week of February 17 05Doing itQrqA ChargeThe spot where we wantto know the Electric FieldunitunitrQkqrqQkrFErF22FElectric Field 22Week of February 17 05General-unitjjjjjunitunitrQkqGeneralrQkqrqQk,222rFEErFErFElectric Field 23Week of February 17 05Continuous Charge DistributionElectric Field 24Week of February 17 05 ymmetryElectric Field 25Week of February 17 05Let’s Do it Real TimeConcept – Charge perunit length dq=  dsElectric Field 26Week of February 17 05The math)sin(2)cos(2)cos()2()cos()2(0000202000rkdrkErrdkErdqkEErddsxxxyWhy?Electric Field 27Week of February 17 05A Harder ProblemA line of charge=charge/lengthsetupsetupdxLrxdEdEyElectric Field 28Week of February 17 052/02/3222/02/322222222)(2)(2)()cos()()cos(LxLxLLxxrdxkrExrdxrkExrrxrdxkE(standard integral)Electric Field 29Week of February 17 05Completing the MathrkLrklELrLLrrkLExx224:line long VERY a oflimit In the4:nintegratio theDoing22221/r dependenceElectric Field 30Week of February 17 05Dare we project this??Point Charge goes as 1/r2Infinite line of charge goes as 1/r1Could it be possible that the field of an infinite plane of charge could go as 1/r0? A constant??Electric Field 31Week of February 17 05The GeometryDefine surface charge density=charge/unit-areadq=dAdA=2rdr(z2+r2)1/2dq= x dA = 2rdrElectric Field 32Week of February 17 05(z2+r2)1/2     RzzrzrdrzkErzzrzdrrkrzdqkdE02/3222/122222222)cos(Electric Field 33Week of February 17 05(z2+r2)1/2Final Result0z2202E,R 12WhenRzzEzElectric Field 34Week of February 17 05Look at the “Field Lines”Electric Field 35Week of February 17 05What did we learn in this chapter??We introduced the concept of the Electric FIELDFIELD.We may not know what causes the field. (The evil Emperor Ming)If we know where all the charges are we can CALCULATE E.E is a VECTOR.The equation for E is the same as for the force on a charge from Coulomb’s Law but divided by the “q of the test