19.3 Coulomb’s Law 19.2 Insulators And Conductors Forces .

Chapter 19 Electric Charges,Forces, and Fields19.119.219.319.419.519.6Electric ChargesInsulators and ConductorsCoulomb’s LawThe Electric FieldElectric Field LinesShielding and Charging by Induction

Figure 19-1 Charging an amber rodAn unchargedamber rod (a)exerts no force onscraps of paper.When the rod isrubbed against apiece of fur (b) itbecomes chargedand then attractsthe paper (c).

Figure 19–2 Likes repel, opposites attractA charged amber rod issuspended by a string. Accordingto the convention introduced byBenjamin Franklin, the charge onthe amber is designated asnegative. (a) When anothercharged amber rod is broughtnear the suspended rod it rotatesaway, indicating a repulsive forcebetween like charges. (b) When acharged glass rod is broughtclose to the suspended amberrod, the amber rotates towardthe glass, indicating an attractiveforce and the existence of asecond type of charge, which wedesignate as positive.

Figure 19–3 The structure of an atomA crude representationof an atom, showingthe positively chargednucleus at its centerand the negativelycharged electronsorbiting about it. Moreaccurately, theelectrons should bethought of as forminga "cloud" of negativecharge surrounding thenucleus.

All of these attractive or repulsive ELECTROSTATIC forcesare due to electrical charges in the atoms of the materials. Sincethere are two types of force there must be two types of charge!Both protons and electrons have the same charge. BUT, It is Positive forthe Proton and Negative for the Electron.Proton charge, ep 1.6x10-19 CElectron charge, e -1.6x10-19 CAn atom is neutral because # protons # electronsProton mass, mp 1.67x10-27 kgElectron mass, me 9.11x10-31 kgCharge is QUANTIZEDCharge on an object, Q NeIt only exists in discrete units

Charge is CONSERVEDThe net charge in a closed system is constant.It can be moved around, howeverCharge is measured in Coulombs1 C is a lot of charge1 µC 10-6 C 0.000001 CProblem: Charge is QuantizedA amber rod is rubbed with fur and acquires a charge of –4.8 µC.AHow many electrons does it gain?BDoes the fur gain or lose electrons? How many?Charge is ConservedA glass rod rubbed with silk acquires a charge of 8x10-9 C.AWhat is the charge on the silk?BIs the glass rod heavier or lighter after rubbing?CIs the silk heavier or lighter after rubbing?

19.2Chargesmoveeasilythroughthem.CONDUCTORS AND INSULATORSConducts electricityCONDUCTORCan conduct electricity a littleSEMICONDUCTORCan charge byrubbingDo not conduct electricityINSULATORCharges on an insulator DONOT move through theinsulator. Proof:?

Charging an insulator by rubbing it with another insulator.ONLY electrons can move between materials.If an object (insulator) becomes positively charged by rubbing.It means that it has LOST electrons.The material used for rubbing has gained electrons.It is the large amount of energy from the rubbing that removes theelectrons from the insulator.

Figure 19–4 Charge transferInitially. an amberrod and a piece offur are electricallyneutral. As they arerubbed together,charge is transferredfrom one to theother. In the end, thefur and the rod havecharges of equalmagnitude butopposite sign.

Figure 19–5 Electrical polarizationWhen a charged rod is far from aneutral object the atoms in theobject are undistorted, as in Figure19–3. As the rod is brought closer,however, the atoms distort,producing an excess of one type ofcharge on the surface of the object(in this case a negative charge).This induced charge is referred toas a polarization charge. Since thesign of the polarization charge is theopposite of the sign of the chargeon the rod, there is an attractiveforce between the rod and theobject.

A charged insulator causes an uncharged insulator to become polarized.The atoms in the insulator are neutral but the charges within them can move around.A charged insulator ALWAYS attractsuncharged insulators.It does not matter if it is positively ornegatively charged.

Figure 19–6 Charging a conductorWhen an unchargedmetal sphere is touchedby a charged rod (a)some charge istransferred at the point ofcontact. Because likecharges repel, andcharges move freely on aconductor, the transferredcharge quickly spreadsout and covers the entiresurface of the sphere (b).

Figure 19–7 Forces between pointchargesNotice that in eachcase the forcesexerted on the twocharges form anaction–reaction pair.Thus, the force thatcharge 1 exerts oncharge 2 is equaland opposite to theforce that charge 2exerts on charge 1.

How Big Are The Forces Between Charges?In 1769, John Robison found that if you double the distance betweencharges then the force between them is reduced by 4.In 1785 Coulomb showed:kq qF 12 2rwhere21Nmk 8.99x10 94πε 0C2Force, F is in Newtons, NCharge is in Coulombs, Cr is in meters, m F12 F21 Directions are opposite, however.Do not worry about the sign of the chargeswhen calculating the forces between charges.The direction of the forces on charges followsfrom the fact that opposite charges attract andlike charges repel.

Figure 19–8 Superpositiona) Forces areexerted on charge 1by the charges 2, 3,and 4. These forcesare F12, F13, and F14respectively. (b) Thenet force acting oncharge 1, which welabel F1, is the vectorsum of F12, F13, andF14.

Worked example: Similar to problems 22-23 and 54A.What is the force (magnitude and direction) on q3The force is along the line joining the charges.The direction depends on the sign of the charges.Two charges will give rise to two forces on q1.Remember: Forces add as vectors.

The Electric FieldElectric forces appear to act through empty space. Just like gravitational forces.A charge in space creates an electric field. Just like the earth creates a gravitationalfield in the space around it.A second charge in the vicinity of the first experiences a force because of the electricfield. Just like a second mass near the earth experiences a force because of the fieldof the earth.The electric field is a vector and points in the direction of the force that a positive“test” charge would feel.For gravitation we describe how these forces vary in space by using theconcept of GRAVITATIONAL FIELD.For example, the earth produces a gravitational field. A mass, such as theplanet Mercury, is attracted to the earth. But the size of this attractiondepends on how far Mercury is from earth. The distance between Mercuryand earth varies as Mercury moves so the attraction will vary. We say thatMercury experiences a force due to the earths gravitational field.

Figure 19–9 An electrostatic force fieldThe charge q at theorigin of thiscoordinate systemexerts a differentforce on a givencharge at everypoint in space. Herewe show the forcevectors associatedwith q for a grid ofpoints.

Figure 19–9B The Electric FieldPlace test charge, q0 at variouspoints near the charge q. The forceat each point varies in magnitudeand direction. The size of the forcedepends on the size of the testcharge, q0. If we divide this forceby q0 we get the force per unitcharge at each point in space. Theelectric field due to a charge ordistribution of charges at somepoint in space is defined in termsof the force that a test charge (q0)would experience if it were at thatpoint in space.F/q0 Eequation 19.8

Figure 19–10 The electric field of apoint chargeThe electric field Edue to a positivecharge q at theorigin is radiallyoutward. Itsmagnitude isE kq /r2.For a point charge,E F/q0 kqq0 /r2q0E kq / r2

Figure 19–11 The direction of theelectric field(a) The electricfield due to apositive chargeat the originpoints radiallyoutward. (b) Ifthe charge atthe origin isnegative, theelectric field isradially inward.

Figure 19–12 Superposition ofthe electric fieldThe net electric fieldat the point P is thevector sum of thefields due to thecharges q1 and q2.Note that E1 and E2point away from thecharges q1 and q2respectively. This isas expected, sinceboth of thesecharges are positive.

Figure 19–14 Electric field linesfor a point charge(a) Near a positive charge thefield lines point radially awayfrom the charge. The lines starton the positive charge and endat infinity. (b) Near a negativecharge the field lines pointradially inward. They start atinfinity and end on a negativecharge and are more densewhere the field is more intense.Notice that the number of linesdrawn for part (b) is twice thenumber drawn for part (a), areflection of the relativemagnitudes of the charges.

Figure 19–15 Electric field lines forsystems of charges(a) The electric field lines for a dipole form closed loops that becomemore widely spaced with distance from the charges. (b) In a systemwith a net charge, some field lines extend to infinity. If the chargeshave opposite signs, some field lines start on one charge andterminate on the other charge. (c) All of the field lines in a system withcharges of the same sign extend to infinity.

Properties of Electric Field Lines (Lines of force)1234They do not cross. WHY?The # of field lines leavinga positive charge equals the# of field lines entering anegative charge.Field lines are usuallycurved. They are onlystraight for a point chargeor in a parallel platecapacitor.Electric field lines points inthe direction of the forcethat a positive “test” chargewould experience.Problem 37: The electric field linessurrounding three charges is shown.The center charge, q2 -10 µC. Whatare the signs of the other two charges.Find q1 , q3

Consider also example 19.2ExampleE6µCE1.5µCq0Can E 0 to the left of q1?Can E 0 to the right of q2?If E 0 at some position it means that the force on a positive test chargeat that position is zero.

ProblemTwo charges, –3 µC and –4 µC are located at (-0.5 m, 0) and (0.75 m, 0), respectively.(A) Where on the axis is the electric field zero?q1 -3 µC-0.5q2 -4 µCd00.75

Figure 19–17 A parallel-platecapacitorIn the idealcase, theelectric fieldis uniformbetweenthe platesand zerooutside.

Figure 19–17b A parallel-platecapacitorCharge on plate -QCharge on plate QEE Q / ε0 A σ / ε0 4πk Q/ ΑEENoteNo distance dependenceE is constant between the platesSee page 636Plates have area, A

Figure 19–18 Charge distributionon a conducting spherea) A charge placed on a conductingsphere distributes itself uniformly onthe surface of the sphere; none of thecharge is within the volume of thesphere. (b) If the charge weredistributed uniformly throughout thevolume of a sphere, individualcharges, like that at point A, wouldexperience a force due to othercharges in the volume. Since chargesare free to move in a conductor, theywill respond to these forces by movingas far from one another as possible;that is, to the surface of the conductor.

Figure 19–19 Electric field near aconducting surface(a) When an uncharged conductor isplaced in an electric field, the fieldinduces opposite charges onopposite sides of the conductor. Thenet charge on the conductor is stillzero, however. The induced chargesproduce a field within the conductorthat exactly cancels the external field,leading to E 0 inside the conductor.This is an example of electricalshielding. (b) Electric field lines meetthe surface of a conductor at rightangles. That is, electric field lines areALWAYS perpendicular to theconductor surface.

Figure 19–20 Intense electricfield near a sharp pointElectric charges andfield lines are moredensely packed near asharp point. Thismeans that the electricfield is more intense insuch regions as well.(Note that there are noelectric charges on theinterior surfacesurrounding the cavity.Chargeconcentrates at curvedsurfaces ofconductors.WHY?

Chargeconcentrates atcurvedsurfaces ofconductors.WHY?

Electric fields do not exist inside conductors, ever. - Faraday CageElectric field lines are ALWAYS perpendicular to the conductor surface.No E-field insideconducting sphere

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Figure 19–21 Shielding works inonly one directionA conductordoes not shieldthe externalworld fromcharges itencloses. Still,the electric fieldis zero within theconductor itself.