Electric Charge Electromagnetism 10 20 14 9 18 AM Study of physical laws that govern the interaction between charged particles and between currents moving charge 1 Stationary charges electrostatics 2 Moving charges electrodynamics 3 Leads to understanding of nature of light Basic concepts Electrical charge o Property of material particles like mass Difference charge can come in two flavors ve positive and ve negative unlike mass Different laws for interaction between charges than in masses gravitational force electron o mass 9 1 10 31 kg o Charge e 1 6 10 19 Coulombs one quantum of charge smallest natural free form charge Proton neutron o mass 1 67 10 27 kg o e 1 6 10 19 Coulombs o mass 1 67 10 27 kg o charge 0 Principle One electrical charge is charge is quantized o macroscopic charge q or n e where n 1 2 3 Principle Two Conservation of charge o Algebraic sum of charges in a closed system is constant charge can NOT be created or destroyed but can be transferred o Transfer of charge happens through flow of electrons Conductors Allow free flow of electrons Insulators do NOT allow free flow of electrons Electric Charge 1 Quantized q or n e where n integer 2 Conserved Macroscopic Observation of charges Charging by conduction touching a charged object to another object Charging by induction bringing a charged object near another object to cause the opposite charge to pull further from the rest of the object Negatively charged metal sphere and bring an uncharged sphere next to it there will be an attractive force If you touch them together the electrons will spread out and there will be only a repulsive force Coulomb s Law 1784 Torsion Balance experiment If two point charges separated by a distance r then there is a force between them is proportional to 1 r 2 and Force is proportional to the magnitude of q1 q2 Coulomb s Law o F k q1 q2 r 2 o F k q1 q2 r 2 where r hat is the unit vector of magnitude one and equals r vector r and F k q1 q2 r 3 r o SI units of charge r meters F Newtons charge q Coulombs units of k N m 2 C 2 o k 9 x 10 9 N m 2 C 2 k 1 4 Pi 0 where 0 8 8 x 10 12 C 2 N m 2 electrical permittivity in a vacuum Electrical force is a vector and acts along the shortest straight line joining two charges forces will be on the same charge Forces are equal and opposite between the two charges F 12 is the force vector on one due to two F 21 is the force vector on two due to one F 21 F 12 Electrical forces Coulombs Law If more than two charged objects just add forces pairwise Principle of Superposition o Force acting on a given charge by a number of other charges can be added vectorially to find the resultant force on that charge Basically just do it separately then add together at the end EX Coulomb s Law However if you have a continuous body of charge you integrate F net following Example Two point q1 q2 2 0 C micro coulombs located at x 0 y and 0 3 m Third point charge q3 4 0 C located at x 0 40 m and y 0 Find total force on q1 Electric Field visualize the force field how forces are communicated between charges within a field EX The charge q generates an electric field E around it When a test charge q0 is placed in that field it experiences force F q0 E E F q0 units are Newtons per Coulomb N C but be careful because adding a charge causes the field to change E lim q0 approaches zero of F q0 so the q0 doesn t disrupt the field but for now electrostatics fixed positions we don t need the limit definition Superposition of electric fields Electric Field expression ONLY FOR A point charge Example touching a doorknob and seeing a spark E 3 10 6 N C breaks down the air 9 10 9 q r 2 so at a given distance can calculate your charge 10 11 electrons xxx coulombs Another way to represent an electric field now with interactions Electric Field Lines imaginary helper lines Electric field lines go away from positive charge Tangent to lines gives direction of E The density of lines gives field strength number of lines not boldness of individual lines Electric field lines E field lines never intersect o If two lines were to intersect then there would be two electric field forces from one object at one point and that doesn t make sense F qE o If the charges are the same sign they repel and if opposite signs they attract F 0 means attractive and F 0 means repulsive Dipole moment p q d where d ALWAYS points from the negative to the positive charge E p 4 Pi epsilon0 r 3 Exercise Prove that E parallel above and what happens if x d Continuous Charges 10 20 14 9 18 AM If several point charges then E is just the sum of 1 4 Pi epsilon qi r unit r 2 EXAMPLE Uniform Line Charge o dq lambda dy o dE1 dE2 o y components cancel dE x 1 4 Pi epsilon lamda dy 1 x 2 y 2 cos theta 2 Case 1 x L 2 Case 2 x L 2 Example Two Ring of charge Center z 0 E 0 z a point charge E k 1 4 Pi epsilon 2 Pi a lambda z 2 point charge times circumference Example Three Same set up but a different distance z away from P z a z a Infinite sheet of charge a infinity For two infinite PARALLEL sheets that are oppositely magnitude equal charged E sigma epsilon0 Force due to external fields 10 20 14 9 18 AM Dipole in a uniform field Right hand rule fingers along F then curl to p then thumb points in direction of torque
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