1 Charges 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 neutrons mproton mneutron melectron mproton 1800 melectron qproton qelectron Calling protons and electrons is a convention We could just 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 F k Q1Q2 where k constant 9 0 109 N m2 C2 2 r Q1 Q2 r In SI units the unit of charge is the coulomb C magnitude of charge of electron e 1 602 10 19 C charge 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 N e 1C N 1C 1C 6 3 1018 19 e 1 6 10 C 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 Boulder 2 we 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 Fgrav Gm1m 2 r2 Fcoul kq1q 2 r2 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 r e 90o r r r r Net force Fnet F1 F2 F1 q1 e F2 q2 e k e2 r r In this particular case F1 F2 F 2 r Fnet 2 F Fnet 2 not 2F k e2 r2 Recall Phys1120 Lecture Notes Dubson1 University of Colorado at Boulder 3 F 2 1 F 1 Fnet 2 1 2 F Superposition Principle the net force on a charge due to other nearby charges is the vector sum of the individual forces r r r r r Fnet F1 F2 F3 where F1 net force due to charge 1 etc Now a new concept the Electric field r Surrounding every charge or group of charges is an electric field E it is a vector thing r Definition The electric field E at a point in empty space is a vector quantity which can be measured by r the following procedure place a small test charge q at that point measure the force F on q due to other charges The electric field is r r Fon q E q 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 r even ifrthere is no test mass nearby to measure the pull of earth s gravity F mg r gravitational field on m g m m F 1 GMm GM 2 m m r2 r M earth mass m test mass r distance from m to Earth s center magnitude g What is the E field around a point charge Q Q source charge source of E field q test charge or probe charge source charge Q r r kQ r F 1 kQq E r r q q r2 r2 Phys1120 Lecture Notes Dubson1 test charge q Fon q University of Colorado at Boulder 4 r r is unit vector pointing away from Q gives direction of E r has no units E field around a positive charge points always from the charge and decreases in magnitude with 1 distance r as E 2 r r r Fon q What if the test charge q in E is negative E field still points away from positive source charge q r Q since both F 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 Boulder 5 The total E field due to a collection of charges is the vector sum of the E fields due to the individual charges k Qi r r r r r E total E1 E 2 E3 K E i 2 ri ri i i Why Superposition Principle says that if we place a small test charge q near other charges Q1 Q2 Q3 then the net force on q is r r r r r r r r r Ftotal F1 F2 Ftotal F1 F2 K K E total E1 E 2 K q q q Metals vs Insulators Most 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 …
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