Physics 212 Lecture 2, Slide 1Physics 212Lecture 2Today's Concept:The Electric FieldContinuous Charge DistributionsMusicWho is the Artist?A) Bill FrisellB) Cindy CashdollarC) Daniel LanoisD) Marc RibotE) Tony RiceWhy?She’s coming to Krannert Center for the Ellnora Guitar Festival!!As a matter of fact, all of the chices will be at Ellnora !!!Physics 212 Lecture 2Our Comments1. If your TA doesn’t show up – go to 231/3 (undergrad office) or home page for telephone numbers of discussion and lab masters (see also email from yesterday)2. Please operate only your own clicker3. Unfortunately we really can’t help with PreLecture, Checkpoint or homework questions by email – too many students: Office Hours, your friends4. Don’t panic!Physics 212 Lecture 2, Slide 3Physics 212 Lecture 2, Slide 4Your CommentsThe concept of infinite line of charge is difficult, especially with the complex integrals.I'm sort of lost with all of this...Are the points on an electric field positive or negative? How do you know when a point moves towards the dipole and when it doesn't move towards the dipole? I am so confused about these. Please go over them in lecture. THANK YOU!the two lines of charge checkpoint confused meCould you please go over the third checkpoint question. I was confused on how to get the correct formula!04Can you elaborate on the creation of electric fields. Does a charge create an electric field on a point? I just don't know how to word everythingCan we go over homework problems in class?I find a lot of these concepts difficult, but I think they will make more sense once I practice problems with them.See example problem at end of lectureWe’ll go over the CheckPointsWhat’s an electric field?Physics 212 Lecture 2, Slide 533q1q2q3q4F2,1F3,1F4,1F1F2,1F3,1F4,1F1F2,1F3,1F4,1F1F2,1F3,1F4,1F1q1q2q3q4Coulomb’s Law (from last time)If there are more than two charges present, the total force on any given charge is just the vector sum of the forces due to each of the other charges:+q1-> -q1fl direction reversed1FMATH:1 31 2 1 412 13 142 2 212 13 14ˆ ˆ ˆ= + +kq qkq q kq qr r rr r r31 2 412 13 142 2 21 12 13 14ˆ ˆ ˆ= + +kqF kq kqr r rq r r r1E≡Physics 212 Lecture 2, Slide 6Electric FieldThe electric field Eat a point in space is simply the force per unit charge at that point. Electric field due to a point charged particleSuperpositionq2q3q4E2E3E4E08FEq≡2ˆQE k rr=2ˆiiiiQE k rr=∑Field points towardnegative andawayfrom positive charges.“Electric fields and also their use with lines of charge really confuse me! ““How fields add together“Physics 212 Lecture 2, Slide 7simulation09Checkpoint 1“Field directions were confusing.” Two equal, but opposite charges are place on the x axis. The positive charge is placedto the left of the origin and the negative charge to the right, as shown in the figure above.What is the direction of the electric field at point A?A. Up B. Down C. Left D. Right E. ZeroWhat is the direction of the electric field at point B?A. Up B. Down C. Left D. Right E. ZeroPhysics 212 Lecture 2, Slide 812Checkpoint 2EEIn which of the two cases below is the magnitude of the electric field at the point labeled Athe largest?same“The magnitudes are equal, only the direction is different. Case one is down and to the right while case two is up and to the right.”Physics 212 Lecture 2, Slide 9Two ChargesTwo charges q1and q2are fixed at points (-a,0) and (a,0) as shown. Together they produce an electric field at point (0,d)which is directed along the negative y-axis.xyq1Eq2(-a,0)(a,0)(0,d)Which of the following statements is true:a) Both charges are negativeb) Both charges are positivec) The charges are opposited) There is not enough information to tell how the charges are related22Physics 212 Lecture 2, Slide 10--++-+23Physics 212 Lecture 2, Slide 1112Checkpoint 3“although the force is double for the right charge for being 2Q, the force is also quartered for being 2r away. ““The distance is squared in the denominator. For the +Q, that leaves 1/1. for the +2Q, that leaves 2/4=1/2. The +Q is therefore stronger in this instance.”“the 2q is 2r away and the q is r away, so the twos cancel out and the test charge will have the same amount of force from each side”INTERESTING: statement is correct, but given in support of “to the left” !!A positive test charge q is released from rest at a distance r away from a charge of +Q and a distance 2r away from a charge of +2Q. How will the test charge move immediately after being released?A. To the left B. To the right C. Stay still D. OtherPhysics 212 Lecture 2, Slide 12ExampleCalculate E at point P.2ˆiiiiQE k rr=∑20“Just some more examples would be cool”What is the direction of the electric field at point P, the unoccupied corner of the square?d+q+q-qPd(A)(B)(C)(D)0=ENeed to know dNeed to know d & q(E)( )2242xq qE k cosddπ  = −   ( )2242yq qE k sinddπ  = −   Physics 212 Lecture 2, Slide 13Continuous Charge DistributionsSummation becomes an integral (be careful with vector nature)λ = Q/L252ˆiiiiQE k rr=∑2ˆdqE k rr=∫“my head is spinning, what does the dQ mean?”WHAT DOES THIS MEAN ??Integrate over all charges (dq)r is vector from dq to the point at which E is definedpt for ELinear Example:chargesdq = λdxrdEPhysics 212 Lecture 2, Slide 14Charge Density• Linear (λ=Q/L) Coulombs/meter• Surface (σ = Q/A) Coulombs/meter2• Volume (ρ = Q/ V) Coulombs/meter3What has more net charge?.A) A sphere w/ radius 2 meters and volume charge density ρ = 2 C/m3B) A sphere w/ radius 2 meters and surface charge density σ = 2 C/m2C) Both A) and B) have the same net charge.28“What exactly is charge density, how is it calculated?”334RVQAπρρ==24 RAQBπσσ==Some Geometry24 RAsphereπ=334RVsphereπ=RLAcylinderπ2=LRVcylinder2π=RRRQQBAσρπσπρ3142334==Physics 212 Lecture 2, Slide 1529Checkpoint 4Both lines have identical charge densities +λ C/m. Point A is equidistant from both lines and Point B is located above the top line as shown. How does EA, the magnitude of the electric field at point A compare to EB, the magnitude of the electric field at point B?A. EA< EBB. EA= EBC. EA> EBTwo infinite lines of charge are shown below.“Since A is located in between two equally charged lines, the electric field in between cancels to 0 at A's