1Charges, Coulomb’s Law, and Electric Fields Some experimental facts:Fact 1: Electric charge comes in two types, which we call (+) and (-).Atoms consists of a heavy (+) charged nucleus surrounded by light (-) electrons.nucleus = (+) charged protons and (0) charged neutronsmproton mneutron >> melectron (mproton 1800 melectron)qproton = qelectronCalling protons (+) and electrons (-) is a convention. We couldjust have easily called electrons (+) and protons (-), but Ben Franklin chose the other, and we’re stuck with it.Fact 2: Unlike charges attract; like charges repel according to Coulomb’s Law: The force F between two charges Q1 and Q2 separated by a distance r is given by Q QF kr=1 22, where k = constant = 9.0 109 N m2/C2 In SI units, the unit of charge is the coulomb (C).magnitude of charge of electron = e = +1.602 10-19 Ccharge of electron = -e , charge of proton = +e (by convention, the symbol e > 0, always)A coulomb is a huge amount of charge: Number N of e’s in 1 C = ? C CN e C N .e . C18191 11 63 1016 10-�= � = = = ��3) Electric charge is conserved. It is impossible to create or destroy net charge. Except in nuclear or “high-energy” reactions, can never create or destroy electrons, protons, and other charged particles – all Phys1120 Lecture Notes, Dubson1 ©University of Colorado at BoulderrQ1Q22we can do is move them around. In high energy reactions, we can create charged particles from energy (energy = mc2), but particles are always created or destroyed in pairs (+1 and -1) so that net charge is conserved.Aside: As far as we know, only 4 things in the universe are conserved:(1) Energy (2) Linear momentum (p = mv) (3) Angular momentum (spin = L = I)(4) Charge[Not quite true: in high energy physics, there may be other quantities, like “baryon number” that are conserved.]4) e is the fundamental unit of charge. You never find a free particle in nature with charge = fraction of e, always find charge = e or integer multiple of e.1) thru 4) are experimental facts. Why are they true? Why are there 2 kinds of charge, not 3? Why e = 1.6 10-19 C, not 4.2 10-19 C? Why is charge conserved? We don’t know! And to some extent, physicists don’t care. It is the primary goal of physics to describe how nature behaves; a secondary goal is to explain why it behaves that way. (Many theorists are looking to explain why, but no luck yet…)Notice that Coulomb’s law is similar to Newton’s Universal Law of Gravitation:1 2 1 2grav coul2 2Gm m kq qF Fr r,= =Similar, except that there are two kinds of charge, but only one kind (sign) of mass. Gravity is always attractive, but electrical force can be attractive or repulsive.Recall that force is a vector – a mathematical object that has a size (magnitude) and a direction. Forces add like vectors, not numbers.Example: Net force on electron due to two nearby protons, each distance r away, 90o apart.Net force = net 1 2F F F= +r r rIn this particular case, 21 22k eF F Fr= = =r r.netF 2 F not 2F)(=2net2k eF 2r=Recall: Phys1120 Lecture Notes, Dubson1 ©University of Colorado at Boulder -eq1 = +eq2 = +eF1F290o r r3Superposition Principle: the net force on a charge due to other nearby charges is the vector sum of the individual forces:net 1 2 3F F F F ...= + + +r r r r, where 1F net force due to charge 1, etc.=rNow, a new concept: the Electric field.Surrounding every charge (or group of charges) is an electric field Er (it is a vector thing)Definition: The electric field Er at a point in empty space is a vector quantity which can be measured bythe following procedure: place a small test charge q at that point, measure the force Fr on q due to other charges. The electric field is on qFEq=rr E-field at a point is the force per charge on a test charge placed at that point.Note! The E-field exists even if there is no test charge present to measure it. Similarly, a gravitational field surrounds the earth, even if there is no “test mass” nearby to measure the pull of earth’s gravity:on mF mggravitational field gm m� = =rrr, magnitude 2 2G M m G MF 1gm m r r= = = (M = earth mass, m = test mass, r = distance from m to Earth’s center)What is the E-field around a point charge Q? (Q = “source charge” = “source” of E-field, q = “test charge” or “probe charge”)2 2k Q q k QF 1E r rq q r r� �= = =rr Phys1120 Lecture Notes, Dubson1 ©University of Colorado at BoulderFFFnet = (2)1/2 F112rtest charge +qFon qsource charge Q4 (r� is unit vector pointing away from Q, gives direction of Er. r� has no units.)E-field around a positive charge points always from the charge, and decreases in magnitude with distance r as 21Er�.What if the test charge q in on qFEq=rris negative? E-field still points away from positive source charge Q, since bothFr changes direction and q switches sign. E-field points away from positive charges, points toward negative charges. Two different views of interaction between charges: “Action at a distance” vs. “Fields”“Action at a distance” : Coulomb’s Law suggests that two charges exert a force on each other through empty space, instantaneously. But Coulomb’s law is only valid for stationary charges. If charge 1 moves, it takes some time for charge 2 to sense the change. The more modern “field-view” is: Charge 1 creates an E-field around it. Charge 2 feels that field. If Charge 1 moves, it takes some time for the surrounding E-field to change, so takes some time for charge 2 to react.Phys1120 Lecture Notes, Dubson1 ©University of Colorado at Boulder5The total E-field due to a collection of charges is the vector sum of the E-fields due to the individual charges:itotal 1 2 3 i i2i iik QE E E E E rr�= + + + = =� �r r r r rKWhy? Superposition Principle says that if we place a small test charge q near other charges Q1, Q2, Q3,… , then the net force on q istotal 1 2total 1 2 total 1 2F F FF F F E E Eq q q= + + � = + + � = + +r r rr r r r r rK K KMetals vs. InsulatorsMost materials can be classified as metal or insulator (insulator also called dielectric)Metals (Cu, Al, Au, Ag, Fe…) conduct electricity. In metals, some of the electrons (conduction electrons) can move freely thru the metal. If there is an E-field, the conduction electrons move in response to the force F = q E and so a flow of charge, or current, occurs.The inner core electrons are bound strongly to their
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