Q E 1 Charges Coulomb s Law and Electric Fields Some experimental facts Experimental fact 1 Electric charge comes in two types which we call and An atom 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 q is symbol for charge 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 The number of protons in the nucleus of an atom is called Z Z determines the element Z 1 is hydrogen Z 3 is lithium Fact 2 Unlike charges attract and like charges repel according to Coulomb s Law which says that the magnitude F of the force between two charges q1 and q2 separated by a distance r is given by F k q1 q 2 r2 where k constant 9 0 109 N m2 C2 q1 F q2 r q1 F Like sign charges repel F F q2 r Unlike sign charges attract 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 Phys1120 Lecture Notes Dubson University of Colorado at Boulder Q E 2 N e 1C N 1C 1C 6 3 1018 19 e 1 6 10 C Fact 3 Electric charge is conserved The net charge of an isolated system cannot change It is impossible to create or destroy net charge Except in nuclear or high energy reactions you can never create or destroy electrons protons and other charged particles all we can do is move them around In high energy reactions we can create charged particles from energy energy mc2 but the particles are always created or destroyed in pairs 1 and 1 so that the 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 Fact 4 The charge e is the fundamental unit of charge You never find a free particle in nature with charge fraction of e You only find charge e or integer multiple of e Statements 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 G m1m 2 r 2 Fcoul k q1 q 2 r2 Similar except that there are two kinds of charge and 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 an electron due to two nearby protons each a distance r away 90o apart as shown r e 90o r Net force Fnet F1 F2 F1 q1 e F2 q2 e Phys1120 Lecture Notes Dubson In this particular case F1 F2 F k e2 r2 University of Colorado at Boulder Q E 3 Fnet 2F not 2F Fnet 2 k e2 r2 Recall F 2 1 F Fnet 2 F 1 Here we have used the Superposition Principle the net force on a charge due to other nearby charges is the vector sum of the individual forces Fnet F1 F2 F3 where F1 net force due to charge 1 etc The Electric field a new concept Surrounding every charge or group of charges is a thing called an electric field E it is a vector thing Definition The electric field E at a point in empty space is a vector quantity which can be measured by the following procedure place a small test charge q at that point measure the force F on q due to all other charges The electric field at that point is given by E Fon q 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 even if there is no test mass nearby to measure the pull of earth s gravity gravitational field Fon m mg F 1 GMm GM 2 g magnitude g m m r2 r m m M earth mass m test mass r distance from m to Earth s center The electric field is not just an mathematical invention it is real We cannot usually see it or smell it but we can feel it In some situations you can see an electric field visible light is a rapidly oscillating electric field more on that later in the semester What is the E field around a point charge Q Q source charge source of E field q test charge or probe charge Phys1120 Lecture Notes Dubson University of Colorado at Boulder Q E 4 source charge Q test charge q r Fon q E Fon q q kQ 1 kQq r r 2 q r r2 r pronounced r hat is the unit vector pointing away from the origin where Q is r hat has no dimensions Magnitude of the E field due to a point charge Q K Q E k 2 r r If the source charge Q is positive then the E field points away from Q in the direction of r hat If the source charge Q is negative then the E field points toward Q in the direction opposite r hat This G G follows directly from the definition E F q For instance if both Q and q are positive then the force F points away from Q and so does E If Q is negative and q is positive then both F and E point toward Q What if the test charge q is changed from positive to negative Then the direction of the force F and the sign of q both flip which leaves the direction of E unchanged The size and direction of the E field is independent of the test charge The test charge is just an imaginary artifice which we use to measure something which is already there The E field around a positive charge points always from the charge and decreases in magnitude with 1 distance r as E 2 We can represent the E …
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