no tagsLecture 003: Electric Field and Simple Distributions of Charge(Wolfson 20.3-20.4)SteveSekula, 26 August 2010 (created 19 August 2010)Main Goals of this LectureIntroduce the principle of "superposition"Review the field concept and extend it to the electric force and electricchargeDiscuss the field of a point chargeDiscuss the fields due to distributions of chargeDiscuss the electric dipole, one of the most important "simpledistributions"Relevant Physics Simulators:"Electric Field Hockey": http://phet.colorado.edu/en/simulation/electric-hockey Can you use electric charge, correctly positioned, tosteer the ball into the goal?"Electric Field of Dreams": http://phet.colorado.edu/en/simulation/efield Explore the effect of various electric charges not just on eachother, but on the electric field at each point in spaceProblem Solving: Coulomb's LawTo attack a problem involving Coulomb's Law, you need to keep a fewdefinitions in mind: is the force that charge 1 exerts on charge 2 is the charge of the source charge (and is a signed quantity) and General Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) LectureNotesF 12~q 1q 2General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...1 of 6 08/26/2010 08:20 PMis the charge of the target charge (the one on which you are trying todetermine the force)the unit vector always points from the source charge to the targetchargedouble-check any results using what you know about charges:like charges REPELunlike charges ATTRACTLet's setup a problem:QUESTIONS: A 1.0- charge is at , and a - charge is at. What force does the positive charge exert on the negative one?How would the net force change if the distance between the chargestripled?INTERPRET: We identify the - as the one on which we want tofind the force, and thus the charge is the source charge.DEVELOP: We're given coordinates, so let's draw a picture and labelthings. The nice part about this is that the charges lie on the same axis(the x-axis, in this case). With the source charge ( ) to the left of , theunit vector in the direction from to is .EVALUATE: Now we use Coulomb's Law to evaluate the force:This force is at a separation of . If that distance tripled to , then theforce would scale bybringing the force at separation to .Point Charges and the Principle of SuperpositionWhen dealing with more than one pair of charges, you need a strategy forr ^ÖC x :0cm = 1 À1:5 ÖC x :0cm = 3q 1:5 2= À ÖC q :0ÖC 1= 1q 1q 2q 1q 2i ^F r i 34iN: 12~=r2kq q1 2^ =(0:020m)2(9:0 0 N =C )(1:0 0 C)(À1:5 0 C)Â 19Á m2 2Â 1À6Â 1À6^= À^2cm 6cm F =F =(r ) 2cm) =(6cm) =9 01212= r2120122= (2 2= 16cm F 3:8iN 012~= À^General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...2 of 6 08/26/2010 08:20 PMcomputing the force on a charge, , given a number of other charges (where runs from 1 to N and labels each of the remaining charges).Because force is a vector, to find the total force on you add the forces(vectors) exerted on by the charges . The force that exerts on isunaffected by the force exerts on - this allows us to superpose theindividual forces to find the total force. This is not obvious, but its realityhas been upheld by experiments and observations of nature. Nature didn'thave to be this simple, but it is.Why do you need this? Coulomb's Law applies to point charges - chargedobjects whose size is negligible. However, the real world is populated bycharge distributions - a collection of many charges spread out overspace. For instance:molecules are an example of distributions of charges - protons andelectrons - and those distributions matter when you are thinking abouthow different molecules interact with one another (and, since they aresimilarly sized, you cannot neglect their dimensions).your heart contains a charge distribution, which accumulates duringsystole (contraction of the heart) and causes heart muscle tissue tocontract and pump bloodTherefore, we are often confronted with situations where we need to dealwith a distribution of charge.Review of the Field ConceptForces like gravity bothered scientists in the 1600s because you had toinvoke "spooky action at a distance" to explain how, for instance, the earthkept the moon in orbit. The idea of a field relieves the mind of the concernabout a mysterious and unseen contact between two objects; instead, itintroduces the idea that, for instance, the earth creates a gravitationalfield and the moon responds to that field.In gravitation, we talk about the acceleration due to gravity. That can bewritten:The gravitational acceleration can then be thought of as the force per unitmass that an object in Earth's gravitational field would experience. becomes the gravitational field, and it is defined as the force per unit massQ q ii Q Q q iq 1Q q 2Q g =m: ~ = F~g ~General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Documents/Notebooks/PHY1308...3 of 6 08/26/2010 08:20 PMat any point in space around the mass.Electric FieldWe define the electric field similar to the way that you have learned aboutthe gravitational field. It was Michael Faraday (1792-1867)[http://en.wikipedia.org/wiki/Michael_Faraday] who introduced the idea ofan electric force field. Again, he did so to explain the "spooky action at adistance" that objects appeared to experience in the presence of electriccharge.Demonstration: the Van de Graaff GeneratorIf you've never felt an electric field before, after this you'll believe theyexist.Describing the electric fieldThe electric field is given by:the force per unit charge experienced by a charged object at any point inspace. The electric field exists everywhere in space, and we represent thatfield by a series of vectors showing the force experienced by a charge atthe corresponding points in space.Explore the electric field concept through visualization:http://phet.colorado.edu/en/simulation/efieldThe idea of a field can be quite abstract, at first, but it's a useful idea thatpervades physics (in fact, "Quantum Field Theory" is the underlyingmathematical description that we have of nature). In the laboratory, youcan map out the electric force field by measuring the electric force over alarge number of points around a point charge, or a series of charges (e.g.between two sheets of charge).E =q; ~= F~q General Physics - E&M (PHY 1308) - Lecture Notes
View Full Document
Unlocking...