Physics 212 Lecture 3, Slide 1Physics 212Lecture 3Today's Concepts:Electric Flux and Field LinesGauss’s LawMusicWho is the Artist?A) Eric ClaptonB) Bill FrisellC) Jimmy PageD) Jeff BeckE) Buddy GuyWhy?Maybe Someone Less Obscure??Also, my vote for most memorable performance at New Orleans Jazzfest by a big name!Somewhere over the RainbowPeople Get ReadyAmazing….Physics 212 Lecture 3Physics 212 Lecture 3, Slide 3Your Comments“Where did "epsilon not" come from and what is its value?.”042ˆqE k rr=201ˆ4qE rrπε=k = 9 x 109 N m2/ C2εεεε0000= 8.85 x 10-12C2/ N m2IT’S JUST A CONSTANT !“I always understand the material so much better after the lectures and especially the clicker questions”That’s what we hope happens!!“What is the difference between E times A and E "dot" A?” VECTORS: dot product !“Will we ever be expected to take surface integrals, and if so can you discuss them in a little more depth?”“Are we going to actually use calculus now?”“Why is there a specific number of lines coming from a particle? Aren't electric fields radial, so wouldn't the lines be infinite?”Field lines are a REPRESENTATION !You can choose number of lines produced by 1 Coulomb.YOU BET!Integrals will be easy to evaluate, though.. We will use Gauss’ law next time to calculate E fields !!“It's my friend Ben Wallace's birthday tomorrow during the Tuesday lecture! Can you put it on the board for me please?”Physics 212 Lecture 3, Slide 4My Comments• You will need to understand integrals in this course!!!• Forces and Fields are Vectors• Always Draw a Picture First… What do the Forces/Fields Look Like?PrelectureInfinite line of chargeELectureFinite line of charge(constant λ)EWorked ExampleFinite line of charge(non-constant λ)EHomeworkArc of charge(constant λ)E2 201ˆ ˆ4dq dqE k r rr rπε= =∫ ∫WORKS FOR ALL !!“The 1/4 shell problem on the homework was not explained extensively enough in the smart physicsbook.”The “1/4 shell problem” is not special !!It’s the same as all the others!Physics 212 Lecture 3, Slide 5Electric Field LinesDirection & Density of Lines representDirection & Magnitude ofEPoint Charge:Direction is radialDensity α 1/R207Physics 212 Lecture 3, Slide 6Electric Field LinesDipole Charge Distribution:Direction & Densitymuch more interesting…simulation08Physics 212 Lecture 3, Slide 7Preflight 3020406080100“The field lines around charge one are denser, and so its magnitude must also be greater..”Checkpoint 3.1simulation09Physics 212 Lecture 3, Slide 8010203040506070Checkpoint 3.3“The field lines begin at one charge and end at the other. Thus one is positive and the other is negative.”10simulationPhysics 212 Lecture 3, Slide 9Preflight 3020406080100“There is greater density of field lines at point B than point A so the field is stronger at point B.”Checkpoint 3.512Physics 212 Lecture 3, Slide 10Point Charges+2q-qWhat charges are inside the red circle?+Q+Q-Q+2Q-Q-2Q+Q-QABCDE“Telling the difference between positive and negative charges while looking at field lines. Does field line density from a certain charge give information about the sign of the charge?”13Physics 212 Lecture 3, Slide 11Which of the following field line pictures best represents the electric field from two charges that have the same sign but different magnitudes?ABCDsimulation15Physics 212 Lecture 3, Slide 12Electric Flux “Counts Field Lines”SSE dAΦ = ⋅∫Flux through surface SIntegral of on surface SE dA⋅“I still feel a little unclear about flux integrals. Can you go over some more example problems?” 18Physics 212 Lecture 3, Slide 13“flux is proportional to the enclosed charged, and the enclosed charge for case one (lambda*(L))is double the enclosed charge for case two (lambda*(L/2)). ““because the flux is the electric field times the surface area which is 2 pi r times the length. So if the radius is doubled and the length is halved it cancels out to the same .” 01020304050Checkpoint 1(A)Φ1=2Φ2Φ1=Φ2(B)Φ1=1/2Φ2(C)none(D)TAKE s TO BE RADIUS !L/2An infinitely long charged rod has uniform charge density λ and passes through a cylinder (gray). The cylinder in Case 2 has twice the radius and half the length compared with the cylinder in Case 1.23Physics 212 Lecture 3, Slide 14Checkpoint 1(A)Φ1=2Φ2Φ1=Φ2(B)Φ1=1/2Φ2(C)none(D)TAKE s TO BE RADIUS !L/2An infinitely long charged rod has uniform charge density l and passes through a cylinder (gray). The cylinder in Case 2 has twice the radius and half the length compared with the cylinder in Case 1.Definition of Flux:∫⋅≡ΦsurfaceAdEE constant on barrel of cylinderE perpendicular to barrel surface(E parallel to dA)Case 1sE012πελ=LsA)2(1π=01ελL=ΦCase 2)2(202sEπελ=sLLsAππ22/))2(2(2==02)2/(ελL=ΦRESULT: GAUSS’ LAWΦ proportional to charge enclosed !““because the flux is the electric field times the surface area which is 2 pi r times the length. So if the radius is doubled and the length is halved it cancels out to the same .” ” WHAT IS WRONG WITH THIS REASONING??THE E FIELD AT THE BARREL SURFACE IS NOT THE SAME IN THE TWO CASES !!barrelbarrelEAAdE =∫=Φ26Physics 212 Lecture 3, Slide 15Direction Matters:0SSE dAΦ = ⋅ >∫dAdAdAdAdAEEEEEEEEEFor a closed surface, A points outward29Physics 212 Lecture 3, Slide 16Direction Matters:0SSE dAΦ = ⋅ <∫dAdAdAdAdAEEEEEEEEEFor a closed surface, A points outward30Physics 212 Lecture 3, Slide 17Trapezoid in Constant Field0ˆE E x=Label faces:1: x = 02: z = +a3: x = +a4: slanted0EyzDefine Φn= Flux through Face nABCΦ1< 0Φ1= 0Φ1> 0ABCΦ2< 0Φ2= 0Φ2> 0ABCΦ3< 0Φ3= 0Φ3> 0ABCΦ4< 0Φ4= 0Φ4> 0x123dAE0<⋅AdE31Physics 212 Lecture 3, Slide 18Trapezoid in Constant Field + Q0ˆE E x=Label faces:1: x = 02: z = +a3: x = +aDefine Φn= Flux through Face nΦ = Flux through TrapezoidABCΦ1increasesΦ1decreasesΦ1remains sameAdd a charge +Q at (-a,a/2,a/2)+QHow does Flux change?ABCΦ increasesΦ decreasesΦ remains sameABCΦ3increasesΦ3decreasesΦ3remains samexyz0Ex12336Physics 212 Lecture 3, Slide 19QGauss LawdAdAdAdAdAEEEEEEEEEoenclosedsurfaceclosedSQAdEε=∫⋅≡Φ41Physics 212 Lecture 3, Slide 20020406080100“The charge is still located inside of the surface, so the flux does not change.“Checkpoint 2.3(A)Φ increases(B)Φ decreases(C)Φ stays same43Physics 212 Lecture 3, Slide