PHYS 2212K: The Charge Model - Coulomb's Law
PHYS 2212K: The Charge Model - Coulomb's Law
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Y 39Pbysjcs 2212K Chapter 25 255 P HY S I C 5 run SCIENTISTS AND ENGINEERS an mm um i w A STRATEGIC APPROACH 251 The Not So Free Of Charge Model And Other Charge MOdel Electric phenomena seem mysterious at Stuff About Electricity rst but we ll nd that we can under stand them in terms of a charge model I There are two kinds of charge called positive and negative I Two charges of the same kind repel two opposite Charges attract Most charge interactions occur when to objects are I small 69 Obj are meted 0 a charge of e1thers1gn Charges are in everything 0 They shock and attract to us literally rubbing together naughty You39ll learn how Why is this so and to what extent to the charges do so acombrubbed 39 th h h 39 o You Will know by the end piggsap gig 3quot pieces of paper Charges The following diagram shows the relation between creating an interaction between two Discovering electricity l O eCt Experiment 1 Experiment 2 Experiment 3 Experiment 4 with d iffe re nt Rods that haven t electrical been rubbed Plastic rubbed with wool increased distance if Pl SllC Effv a Glass rubbed Ch a rg es quot j quot with sillt quot If quot Plastic AS we ca n Take a plastic rod that has been Rub both plastic rods with Bring a glass rod that has been Further observations show that undisturbed for a long period wool Now the hanging rod rubbed with sillt close to a hang I These forms are gleam for see of time and hang it by a thread tries to move away from the ting plastic rod that has been rods that have been rubbed Pick up another undisturbed handheld rod when you bring rubbed with wool These two more vigorously ru b b n 9 plastic rod and bring it close to the two close together Two rods attract each other g the hanging rod Nothing hap glass rods rubbed with silk l The Slrellglll if me forelis th e r0 d pens to either red also repel each other agaig g with different objects with different electrical charges effected the rods overall net charge When no forces a push or pull are experienced in Experiment 1 we say the objects are neutral Rubbing the rods also very naughty causes there to be a force exerted between them 0 This process is called charging I We call the rubbed rod charged Experiment 2 is known as a longrange repulsive charge since the two objects require no contact and the two rods have been charged the same way 0 This along with Experiment 4 also proves that the force between two charged objects depend on the distance between them Experiment 3 shows the idea of attraction or the coming together of two objects 0 The diagram below simplifies the process exhibited in Experiment 3 One quick note to pick up on about charged objects is that they pick up small pieces of paper This simple test provides a simple answer whether an object is charged or not As we can see by the Experiment 5 the charged rod doesindeed pick up small pieces of paper These ideas set the first stages of what is known as the charge model Discovering electricity Charged rod quot W gtPaper are 4 Charged rod Neutral rod ire Charged plastic rod Silk used to Wool used to rub glass rub plastic i39 x JUICE f 39 39 c 1 4 x e 6 5 Charged Charged plastic glass nod rod Charged object Experiment 5 Hold a charged ie rubbed plastic rod over small pieces of paper on the table The pieces of paper leap up and stick to the rod A charged glass rod does the same However a neu tral rod has no effect on the pieces of paper Experiment 6 Rub a plastic rod with wool and a glass rod with silk llang both by threads some distance apart Both rods are attracted to a neutral to unrubbed plastic rod that is held close Interestingly both are also attracted to a neutral glass rod ln fact the charged rods are at tracted to any neutral object such as a finger a piece of paper or a metal rod Experiment 7 Rub a hanging plastic rod with wool and then hold the wool close to the rod The rod is weakly attracted to the wool The plastic rod is repelleal by a piece of silk that has been used to rub glass Experiment 8 Further experiments show that I Other objects after being rubbed attract one of the hanging charged rods plastic or glass and repel the other These objects always pick up small pieces of paper I There appear to he no objects that after being rubbed pick up pieces of paper and attract both the charged plastic and glass rods The Charge Model Charge model part II The basic postulates of our mettle are ll Frictiohal forces such as rubbing add something called charge to art object If an Oblect ls Charged39 It always er retrieve it from the object The process itself is called charging More vig attracts to one Charged rod and repels ereus rubbing produces a larger quantity of charge the other We either say it acts There are twe arid ertly twe kinds cf charge Fer new we will call these plastic charge and glass charge Other ehjects cart semetimes he charged by rah hittg but the charge they receive is either plastic charge er glass charge 9355 either quot like plasticquot or quot like 3 Twe like charges plasticplastic er glassglass exert repulsive forces eh each ether Twe opposite charges plasticglass attract each ether 4 The erce between two charges is a l gf g force The size of the fierce increases as the quantity cf charge increases and decreases as the distance between the charges increases 5 Neutral ehjects have arr equal mixture e f heth plastic chargequot and glass charge The ruhhihg precess semehew marriages tie separate the twe Electric Properties of Materials Discovering electricity lll The metal Experiment 9 sphere accptires plastic clziarge 1 M r l x E 1 Charge a plastic rod by rubbing it with wool Touch a neutral metal sphere with quotthe Charged rubbed area of the rod The metal sphere then picks up small pieces of paper and repels quott lastic p charged hanging plastic rod The metal sphere appears to have acquired plastic chargr Rod that had Experiment 10 39 u been Charged Charge a plastic rod then run your finger along it After you ve done so the rod no longer picks up small pieces of paper or repels a charged hanging plastic rod Similar P the metal sphere of Experiment 9 no longer repels the plastic rod after you touch it wit 1de your finger 39Qm a This sphere Experiment 11 Metal etal termtins l I Place two metal spheres close together with a plastic rod connecting them Charge a neu ra 39 ChmSad second plastic rod by rubbing and touch it to one of the metal spheres Afterward ht was metal sphere that was touched piclcs up small pieces of paper and repels a charged hat ing plastic rod The other metal sphere does neither Experiment 12 This splziere letal Meta aiP l br 1 Repeat Experiment l l Wllfth a metal rod connecting the two metal spheres Touch one aquot I metal sphere with a charged plastic rod Afterward both metal spheres pick up small t39 p astic pieces of paper and repel a charged hanging plastic rod Charges can be transferred from one object to another only when they touch 0 Removing charge form an object by touching is called discharging The two types of materials with different electric properties are called conductors and insulators Charges somehow move through or along a metal rod from one sphere to the other but remain fixedn place on a plastic or glass rod Materials through or along which charge easily move are called conductors 0 Metal Materials where the charge remains immobile are called insulators 0 Glass39 Charge model part ll plastlc 6 There are two types of materials Conductors are materials through or along Note Both which chargeeasily moves Insulators are materials on or in which charges remain fixed in place 39nSUIatorS and 7 Charge can he transferred from one object to another by contact conductors can be charged they differ in the mobmy of the charge 252 Set the Charge And Feel The Pulse If you remember from previous classes there are two types of charges 0 Positive 0 Negative A glass rod that has been rubbed with silk is positively charged 0 We define the terms and using what we learned before anything that attracts to the glass rod is negative while those who attracted it are positive 0 Thus a plastic rod rubbed with wool is negative Protons have a positive charge and electrons have a negative charge Atoms and Electricity FIGURE 251 An atom 39l hc nuclcux cxuggcmml for k lui ll wnlumx pnxim c prolonx nucleus the center to the electron cloud or the of The diagram shows the relation between the field the electrons are in and swarm in the context of an atom a i N m The nucleus IS a compOSIte structure conSIstIng of C l m protons and neutrons o The atom is held together by the attractive 3 electric force between the positive nucleus 39l hc clm39ll39nn cloud ix ncgulivcly charged and the negative electrons The charge like mass is inherently a property of electrons and protons 0 They have charges with different charges but the same magnitude The atomic level unit of charge is called the fundamental unit of charge or e TABLE 251l Protons and electrons Particle Mass kg Charge Proton 16 X I39D 3 15 Electron 91 X I39D 339 e The MicroMacro Connection Electrons and protons are the basic charges of ordinary matter 0 They are particles of matter 0 Their motions are governed by Newton39s laws 0 Electrons can move from one object to another when the objects are in contact but neither electrons nor protons can leap through the air from one object to another A charge is represented by the symbol q q Npe NEE Np 1 N jg Np and Ne are the number of protons and electrons in the object 0 Most macroscopic objects have and equal number of protons and electrons and therefor have C O This is an object with no net charge or electrically neutral An object is positively charged if Np gt Ne An object is positively charged if Ne gt Np An object39s charge is always an integer multiple of e o The amount of charge on an object varies by small but discrete steps not con nuoudy o This is known as charge quantization Objects acquire a positive charge by losing electrons o Protons are extremeytightly bound within the nucleus and cannot be added or removed whereas electrons are bound loosely and can be removed without difficulty The process of removing an electron from the electron cloud of an atom is called ionization 0 When an atom is missing an electron it is called a positive ion The net charge is q e When an atom gains an extra electron it is a negative ion and thus it39s net charge is denoted as q e The process of charging involves rubbing and friction o The forces of friction cause molecular bonds at the surface to break as the two materials slide past each other Molecules are electrically neutral but molecular lFlGllJRE 253 Charging by friction usuallyF creates rnollecular ions as bonds are broken Electrically neutral molecule Atoms if Bond Friction These boncls were broken by friction Positive Negative molecular Hg molecn lar 39 quot ion a i ion a 7V v This ltalf of the molecule ai necl an extra electron as the bond broke This half of the molecule lost an electron as the bond broke ions can be created when one of the bonds in a large molecule is broken 0 The positive ions remain on one material while the negative goes to the other So one ends up with a net positive charge and the other with a net negative charge Charge Conservation and Charge Diagrams The law of conservation of charge states 0 A charge is neither created or destroyed A charge can be transferred from one object to another but the total amount of charge remains constant Like we saw in a previous diagram charging a plastic rod by rubbing it with wool transfers electrons from the wool to the plastic as the molecular bonds break 0 The wool is left with a positive charge equal in magnitude but opposite in sign to the negative charge of the rod qwool 39q plastic 253 Insulators Before Conductors Unless It39s Metal Or Famous Let39s look at insulators and conductors the two classes of materials defined by their electrical properties The diagram to your right shows an insulator o The electrons in the insulator are all tightly bound to the positive nuclei and not free to move around The only way for metals to be ionized is by manipulating the valence elections 0 They are the outer atomic electrons 0 They are known in the solid as a sea of electrons which permeate multiple positively charged ion cores 0 The motion of charges through a material is called a current Charges that move physically move are called the charge carriers Metals remember are conductors Charging Insulators are charged by rubbing o The charge can be FlGURE 2555 An insulatin rod is char e db rubbin transferred to another 9 g l g Negzil ive Clll l g s are immobi e Object upon contact but Rubll l iPlufill l39ml This eacl is oai39lieiod ssuifaee with a piece of aiool w SH Wm 39 Ffj q it doesn39t move around ea30 gffg b 3quot effquot I I u 1 i x V the rod 4 Q Plastic V The posatlae ehai ge Oil The wool is eqaai lo the he game charge oh illTE TDCi Metals cannot be charged by rubbing so they need to be charged by contact with a charged plastic rod The idea behind this stems from the fact that electrons move so once a charge is transferred to the metal repulsive forces between the negative charges cause the electrons to move apart from each other 0 The newly added electrons do not move themselves because the repulsive forces move the entire electron sea a little to the side The sea adjusts very quickly and Ihstantaneousb to the addition or removal of charges 0 Besides this brief interval of adjustment the charge in an I39solaz edconductor are in static equilibrium they are at rest and there is not net force on any charge This is considered electrostatic equilibrium in a conductor are free to FIIGUHIE ZEJE A canductnr is charged by contact with a ChiaF QEd plag tic rod Clz39large i3 tranaferrecl to the metal upon erentaerm Metal Tlhesse changes repel ezieh otlher Clz39large warez1dr ever the s u I39fITICEE39 0f the metal Very 1 fast If there were a net force on one of the charges it would quickly move to an equilibrium point at which the force was zero This electrostatic equilibrium has an important resultant o In an isolated conductor any excess charge is located on the surface of the conductor Discharging The diagram to your right shows the net effect of touching a charged metal o It and the conducting human together become a much larger conductor than the metal alone An object that is physically connected to the earth through a conductor is said to be grounded o The earth is so large that any conductor attached to the earth will be completely discharged Charge Polarization How do charged objects of either sing exert an attractive force on a neutral object Charge polarization is a slight separation of the positive and negative charges in a neutral object lFlGllJlRE 259 Touching a Charged tnetall disehatges it Charges spread tlttaa git the metal h am as system Vety little eltatge is left out the metal FlGURiE 2511 Acharged red polartzesa metal FHGURE 25m A Eharg mid held CI DSE la The sett eteleetthhs is httrheted th the reel lb The eleetrheeepe is pelttrized hy the it an EEEWSCGDE BUSES the leaves and shifts setlztttt there lS KCE SSthegtl l39l ti ehttrged red The seat eteleetthhe Slil llS I ehttrge en the hertr S39tlt39lttce thttetrd the peeittie e red re pie Ba 0 39 Er39 3539 Bring it whirl eel 1e ehttrgeel Lelhee reel elhee th an eleetreeehpe withhttt lD tt itlttg the Sphere ta Peettnre d Metal 3 E III l39 y El 1 is Ii A ele iieit hf eleetreIJS tt net 39 jphsitit39echarge iserettteel TIM 39 y I y hit the 39lttl39S39tlt39lthE m E LC quotmistlle la The rnetttl e Itet ehttrge Altlterttgh the heteherge en the eleetrneeepe is mural WEI till l ll rES is still term but it has been still zerh the letteee httee eheeee peeiti ve ehttrge repel titmitt D l ljt tquot polarized hy the ehttrgetl retell zthtl repel etteh either Whyft quota H o It produces an excess positive charge on the figures shown below Once the electron sea shifts slightly the stationary positive ions begin to exert a force restoring force pulling the electrons back to the right The net force toward the charged rod is called a polarization force o It arises because the charges in the metal are separated not because the rod and metal are oppositely charged In an ianlatecl atnrn the electrnn A negatively charged rod would push the electron sea slightly away polarizing the metal to have a positive upper surface charge and a negative FIGURE 25i12 The polarization tnrce en a neutral piece of metal is due tn the slight charge Separatien 1 The chrngecl red pelarieea the neutral rnetal caneina the In K gt aquot V I tap atn lace ta he negalrve antl V the hattern anrtaee ta be pnaitivec The reel alaci eaerta a a l Wlittht d repnlaive t nrce an the eaeeae paeltive ien carea quot at the hnttam anrfrtee lower surface charge The Electric Dipole quotquot The red eaerte an npvvttrcl attrrtctive farce an the eaceaa electrene at the tap attrTaee 4 Becanae electric tnrce decreaaea vvith cliatance Fm 23 Thna there la a net npaentl farce an the nentrall rnetttl that attracta it tn the jpeaitive reel Two opposite charges with a slight separation between them form what is known as an electric dipole o It shows that an external charge of either sign polarizes the atom to produce an electric dipole with the near end opposite sign to the charge rleunE 2533 A neutral at ll39t i5 p nlarized by an external charge tern39ling an electric dipele Net farce an atnnt Farce an V quot Farce an electrnna I 39 nncleha This eaternal charge 39 pnlariaea the atarn 739 Center at I I 1 Center at negative charge paeltive charge 9 J a The pelariaecl atnrn la an electric tlipnle clnnrl is centered an the nuclena lift 4 hlet three if 1 External chargert 39 I Net three Electric clinnlea can he createrl by either pnai tive nr negative chargea In hath caaea there is an attractive net farce tnwarcl the eaternal charge An insulator has not sea of electrons to shift if an FIGURE 25m The atom in an ingmamr are elarized b an external chair e external charge IS brought close so all the IndIVIdual p F g Pelarigggll pateuns atoms InSIde the Insulator become polarized 3 paperby BC B o Polarizing the atoms in the paper 0 Then exerting an attractive polarization force on Like before remember a charged rod picks up pieces of use later each atom a Net farce Charging by Induction FlGURlE 25115 Charging by induction quot39 I Z39 Z quotW I I t H H quott i t H n J 1 The charged ted pelnt39izes the 2 The lii gttiilr39 ehatge on the eleetresenpe 3 When the red is removed the electroscope person eenclneter is isetated when cantaet is brnken teases first collapse as the The teases repel slightly clue to peltu izttien vanishes then repel pelat izal ien but evetalt the eteel mseepe as the eaeess negative plunge has an excess of electrons and the person spreads out The eleett39escepe has a de cit of eleetrens has been negatively elz latgetl If the person in the diagram removes his or her finger while the system is polarized the electroscope is left with a net negative charge and the person has a net positive charge When the electroscope has been charged opposite to the rod it is a process known as charging by induction 254 Coulomb39s Law And Order Special Forces Unit We found that the electric force decreases with distance the law that describes this behavior is known as Coulomb s Law What Mr Charles Coulomb the quotmath guyquot proved was the electric force obeys an mIersesquare lawwhich is analogous to Newton39s law of gravity Here it is Ceulemb39s law 11 if twc charged particlles having charges am and q are a distance r apart the particles exert ferces eh each ether cf magnitude Kl i ii qul F 2F2tmi F2 252 where K is called the electrostatic constant These ferces are an actiei i reactieri pair equal in magnitude and cppesite ih directien The ferces are directed alcng the time joining the twc particles The tierces are repaisive fer twc like charges and attractive tier twe eppcsite charges FIGURE 2515 Attractive and repulsive fcrces between charged particles We speak of the charges q1 q1 in a literal context 5 TWO objects with a mass size and other things that things h ave Uppesite charges w The law describes the force between charged particles which are known as point charges all o A point charge has a mass and a charge but no size Since we take the absolute value of q which is the magnitude of the force the first part will always be positive but the direction must be determined by the second part of the law Units of Charge The SI unit for charge is the coulomb C The fundamental unit of charge e is equal to is 160 x iii 19C The value for the electromagnetic constant K is K 899 X 109 I sli39mszT2 K 90 x l g N msz2 Now lets39 define yet another new constant yay called the permittivity constant l a 885 x W2 le m2 4wK We can know rewrite Coulomb s law in terms of this constant l lQIllqzl 2 F 4175 r Using Coulomb s Law First off we established that is law is a force law which means that it is a vector 1 Coulomb s law applies only to point charges A point charge is an idealized material object with charge and mass but with no size or extension For practical purposes two charged objects can be modeled as point charges if they are much smaller than the separation between them Electric forces like other forces can lhe superimposed If multiple charges ll 2 3 are present the net electric force on charge due to all other charges is quantity The basic strategies for solving problems using Coulomb s Law are listed Fnct onj Floanj FSIonj II I 254 lPR DBlEIMS DLUING STRATEGHM Electrostatic forces and Coulomb39s law as M lDlEL Identity point charges or objects that can be modeled as point charges ulsusLlZE Use a pictorial representation to establish a coordinate system show the positions of the charges show the force vectors on the charges define dis tances and angles and identify what the problem is trying to nd This is the process of translating words to symbols 50le The mathematical representation is based on Coulomb s law F lon2F20nll r l Show the directions of the forces repulsive for like charges attractive for opposite charges on the pictorial representation ll When possible do graphical sector addition on the pictorial representation While not exact it tells you the type of answer you should expect ll Write each force i rector in terms of its r and ycomponents then add the components to find the net force Use the pictorial representation to deter mine which components are positive and which are negative assess Check that your result has the correct units is reasonable and answers the question 255 Field Of Models Or The Model Of Fields As you know electric or magnetic forces are longrange forces 0 This means no contact is required for one charged particle to exert a force on another 0 This happens instantly because Newton39s law of gravity is not dependent on time The Concept of a Field FIGURE 2523 lron filings sprinkled around the ends of a magnet suggest that the influence of the magnet extends into the space around it l J gt 1 O 0 FIGURE 2512 If charge A metres haw lung lees it take the fierce wetter on B ten respend AG Original FA m E p F d after A on B i l charge A levee Faraday39s concept of a field relates to the G fact that one particle first alters the space around it 39 and the other particle comes along and interacts with the altered space The explicit meaning of a field is a function that assigns a vector to every point in space This concept states that the physical entity exists at every point in space This would explain long range forces The charge makes an alteration everywhere in space The alteration of the space around the mass is called the gravitational fie0 o The space around a charge is altered to create an electric field The difference between a particle and a field is that a particle exists in one point in FllGUFtlE 252a Newton39e and Faredey39s space while a field exists at a points in space The Electric Field heme We describe electric fields by using the field model which describes how charges interact 0 Some charges called source charges alter space around them by creating t an electric field A separate charge in the electric field F eld an El experiences a vector force exerted by the field A probe charge q changes as it moves through space 0 O 0 It39s electric force changes lidE ElS ab Ul39t fang range force5 If1 tte Nee tenian 39tequotiew A exerts a three eliteetly en E If1 Fat acilayja View A altere tlte epaee area th it The wattry linea are peetie lieenae W39e detft Knew what the alteratielit llaelka lilleej Pt tt tiel e B then t E S j t tCllS te tte altered apttee The alteretl apaee ia the agent litat eaerta tte fearee en E It suggests that something is present at each point in space that causes the change in charge q We denote different points on the electric field by using X y Z The equation is given Few at L ye e q Ea y z E It is defined as a forcetoCharge ratio so its units are NC The magnitude E of the electric field is called the electric field strength So if the probe charge q experiences an electric force at a point in space we say that there is an at that point in space l Equation 255 assigns a vector to event point in space That is the electric field is a rector eld Electric field diagrams will show a sarnple of the rectors but there is an electric field sector at every point whether one is shown or not 2 lfq is positive the electric field vector points in the same direction as the force on the charge Because 3 appears in Equation it may seem that the electric field depends on the size of the charge used to probe the field It doesn t We know from Coulomhls law that the force EU is proportional to n Thus the electric field defined in Equation is independent of the charge q that probes the field The electric field depends only on the source charges that create the field When we rearrange the equation and find the force exerted by a known field or when an electric field experiences an electric force by a charge as such e zqze an a FIGURE 2525 Charge er is a precise of the electric field Charge qt heing used as a prehe Dquot a chiage The ferce an r tells us that there s an electric field at peint l Paint l quot eerie 2 New charge qt is placed at point Thereis alse an electric field here that differs fresh the field at peint l h Th is i s the electric field secter at paint 1 h F 54 This is the electric field secter at point 2 The dots are the peints at W h ic h the field is kltD WIZTI If C is positive the force on the particle is in the direction of the electric field If C is negative the force on the particle is opposite to the direction of the electric field The Electric Field of a Point Charge FlGUHlE 2515 Chang a is 590 3 Iiirlil39f E the electric field ef peint charge 339 For this section we will determine the electric field a Whirl r3 EelsElli 3i field ef 3 at this pelntquot of a single point charge q a My Peint charge We need to define q to define the probe of the electric field We define it as la 1 Place g at the peint te prebe the field a I w 39 qur I T away trern a I e 39 k a 2 f e 1 t 2 lvleastlre the ferce en q l We define the electric field in this case as c en i v E If 2awayfretn q q 4174a r v 393 The electric field l a FGH fllfqur q it is a vecter in the dircc tien ef F 39 a en q When we calculate the field at a sufficient number of points in space we draw a field diagram In the diagram below notice all the field vectors point away from charge q o The arrows also decrease in length due to the inverse square dependence on r FlGUFtlE 252 The electric field eta pesitive peint charge Keep these rules in mind ll 39ll39he diagram is just a representative sample ef electric field vecters The field 3391 exists at all the ether peints A welldrawn diagrarn can tell ye u fairly well what the field we uld he like at a neighhering peint 2 The arrew indicates the directien and the strength ef the electric field at the paint r m which it is attached that is at the peint where the mil ef the vecter is placed In this chapter we indicate the peint at which the electric field is measured with a det The length ef any vecter is significant enly relative te the lengths ef ether vecters Altheugh we have te draw a vecter acress the page frern ene peint te anether an electric field vecter is met a spatial quantity It dees net stretch frern ene peint te anether Each vecter represents the electric field at erre paint in space Unit Vector Notation We use unit vectors to express the direction of q 1 l Jr and The unit vector for length denote r with a funny little hat on top that points from the origin to a point of interest 0 It only specifies direction No matter which point you choose the electric field at that point is quotstraight outwardquot from the charge 0 In other words the electric field points in the direction of the unit vector r with a hat We can denote it as a l E r Electric eld of a point charge 47TE1 F I It doesn39t matter if the unit vector is negative itjust changes direction but still points towards charge q IFIGURE 2518 Using the unit vector E a E i e i e The iiiiii veetme eipeeifjiy the diree l39iene re the jpeiiiie h Eieetricfieldetpeini1w quot in iiil direciimti ef Fl quotWu h 391 E2 in he Liireeiimfi ei r3 FIGURE 25329 The electric field of a negative 30th Charge General Principles Coulomb39s Law The forces between two charged particles ql and q separated by distance r are Klailal Flon Z onui These forces are an actionlreaction pair directed along the linejoining the particles I The forces are repulsive for two like charges attractive for two opposite charges I The net force on a charge is the sum of the forces from all other charges I The unit of charge is the coulomb C I The electrostatic constant is K 9611 X ith N mlezi Important Concepts The Charge Modei There are two kinds of charge positive and negative I Fundamental charges are protons and electrons with charge is where g 2 ran X for 19 c Objects are charged by adding or removing electrons I The amount of charge is q 1 Np Nae I An object with an equal number of protons and electrons is neutral meaning no net charge t Like charges repela opposite charges attract 39 Charged objects exert electric forces on each other 1 z I The force increases as the charge increases I The force decreases as the distance increases There are two types of material insulate rs and conductors I Charge remains fixed in or on an insulator I Charge moves easily through or along conductors I Charge is transferred by contact between objects Charged objects attract neutral objects I Charge polarizes metal by shifting the electron sea I Charge polarizes atomsi creating electric dipoles I The polarization force is always an attractive force Iii Net force Polarized neutral objects III Net force External 69 charges 39 E The Field Model Charges interact with each other via the electric field I Charge A alters the space around it by creating an electric field I The field is the agent that exerts a force The force on charge IE is Em fof An electric eld is identified and measured in terms of the force on a probe charge q EF a 39 um I The electric field exists at all points in space I An electric field vector shows the field only at one point the point at the tail of the vector Ni x i f HEM fix J x The electric field of a point charge i llareal r us 39f A E r M