IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

Motivação•Fenômenos eletromagné-ticos (EM) onipresentes:• p.ex., ondas EM: Luz!!! • estabilidade dos átomos: eletrostática• descargas elétricas• m a g n e t i s m o : í m ã s , levitação magnética, etc.

Eletricidade e magnetismo considerados fenômenos disjuntos até a unificação: JC Maxwell, Treatise on Electricity and Magnetism (1873)

Em Fis III:•Eletrostática•Eletrodinâmica•Magnetostática •Variação temporal: indução•Equações de Maxwell

2

Cap.  21  -­‐  Carga  e  Campo  Elétricos21.1  Carga  ElétricaEvidências  experimentais  de  carga  elétrica  (Grécia  c.  600  A.C.):  pedaços  de  âmbar  após  atrito  com  lã  atraem  outros  objetos  (hoje:  melhor  com  bastões  de  plásKco  e  vidro,  atritados  com  pele  e  sêda,  respecKvamente)

IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

than earlier chapters. The reward for your extra effort will be a deeper understand-ing of principles that are at the heart of modern physics and technology.

21.1 Electric ChargeThe ancient Greeks discovered as early as 600 B.C. that after they rubbed amberwith wool, the amber could attract other objects. Today we say that the amber hasacquired a net electric charge, or has become charged. The word “electric” isderived from the Greek word elektron, meaning amber. When you scuff yourshoes across a nylon carpet, you become electrically charged, and you can chargea comb by passing it through dry hair.

Plastic rods and fur (real or fake) are particularly good for demonstratingelectrostatics, the interactions between electric charges that are at rest (or nearlyso). After we charge both plastic rods in Fig. 21.1a by rubbing them with thepiece of fur, we find that the rods repel each other.

When we rub glass rods with silk, the glass rods also become charged andrepel each other (Fig. 21.1b). But a charged plastic rod attracts a charged glassrod; furthermore, the plastic rod and the fur attract each other, and the glass rodand the silk attract each other (Fig. 21.1c).

These experiments and many others like them have shown that there areexactly two kinds of electric charge: the kind on the plastic rod rubbed with furand the kind on the glass rod rubbed with silk. Benjamin Franklin (1706–1790)suggested calling these two kinds of charge negative and positive, respectively,and these names are still used. The plastic rod and the silk have negative charge;the glass rod and the fur have positive charge.

Two positive charges or two negative charges repel each other. A positive chargeand a negative charge attract each other.

CAUTION Electric attraction and repulsion The attraction and repulsion of two chargedobjects are sometimes summarized as “Like charges repel, and opposite charges attract.”But keep in mind that the phrase “like charges” does not mean that the two charges areexactly identical, only that both charges have the same algebraic sign (both positive orboth negative). “Opposite charges” means that both objects have an electric charge, andthose charges have different signs (one positive and the other negative). ❙

688 CHAPTER 21 Electric Charge and Electric Field

++ +

+ +++++

++ + + +

PlasticFur

(a) Interaction between plastic rods rubbedon fur

– – – – –– –

–– –

... but after beingrubbed with fur,the rods repeleach other.

Plain plastic rods neither attract nor repel each other ...

Silk Glass

(b) Interaction between glass rods rubbedon silk

++ + + ++

++

+ +

... but after beingrubbed with silk,the rods repeleach other.

Plain glass rods neither attract nor repel each other ...

(c) Interaction between objects with oppositecharges

++ + + +– – – – –

... and the fur and silkeach attracts the rod it rubbed.

The fur-rubbed plasticrod and the silk-rubbed glass rod

attract eachother ...

21.1 Experiments in electrostatics. (a) Negatively charged objects repel each other. (b) Positively charged objects repel each other. (c) Positvely charged objects and negatively charged objects attract each other.

than earlier chapters. The reward for your extra effort will be a deeper understand-ing of principles that are at the heart of modern physics and technology.

21.1 Electric ChargeThe ancient Greeks discovered as early as 600 B.C. that after they rubbed amberwith wool, the amber could attract other objects. Today we say that the amber hasacquired a net electric charge, or has become charged. The word “electric” isderived from the Greek word elektron, meaning amber. When you scuff yourshoes across a nylon carpet, you become electrically charged, and you can chargea comb by passing it through dry hair.

Plastic rods and fur (real or fake) are particularly good for demonstratingelectrostatics, the interactions between electric charges that are at rest (or nearlyso). After we charge both plastic rods in Fig. 21.1a by rubbing them with thepiece of fur, we find that the rods repel each other.

When we rub glass rods with silk, the glass rods also become charged andrepel each other (Fig. 21.1b). But a charged plastic rod attracts a charged glassrod; furthermore, the plastic rod and the fur attract each other, and the glass rodand the silk attract each other (Fig. 21.1c).

These experiments and many others like them have shown that there areexactly two kinds of electric charge: the kind on the plastic rod rubbed with furand the kind on the glass rod rubbed with silk. Benjamin Franklin (1706–1790)suggested calling these two kinds of charge negative and positive, respectively,and these names are still used. The plastic rod and the silk have negative charge;the glass rod and the fur have positive charge.

Two positive charges or two negative charges repel each other. A positive chargeand a negative charge attract each other.

CAUTION Electric attraction and repulsion The attraction and repulsion of two chargedobjects are sometimes summarized as “Like charges repel, and opposite charges attract.”But keep in mind that the phrase “like charges” does not mean that the two charges areexactly identical, only that both charges have the same algebraic sign (both positive orboth negative). “Opposite charges” means that both objects have an electric charge, andthose charges have different signs (one positive and the other negative). ❙

688 CHAPTER 21 Electric Charge and Electric Field

++ +

+ +++++

++ + + +

PlasticFur

(a) Interaction between plastic rods rubbedon fur

– – – – –– –

–– –

... but after beingrubbed with fur,the rods repeleach other.

Plain plastic rods neither attract nor repel each other ...

Silk Glass

(b) Interaction between glass rods rubbedon silk

++ + + ++

++

+ +

... but after beingrubbed with silk,the rods repeleach other.

Plain glass rods neither attract nor repel each other ...

(c) Interaction between objects with oppositecharges

++ + + +– – – – –

... and the fur and silkeach attracts the rod it rubbed.

The fur-rubbed plasticrod and the silk-rubbed glass rod

attract eachother ...

21.1 Experiments in electrostatics. (a) Negatively charged objects repel each other. (b) Positively charged objects repel each other. (c) Positvely charged objects and negatively charged objects attract each other.

than earlier chapters. The reward for your extra effort will be a deeper understand-ing of principles that are at the heart of modern physics and technology.

21.1 Electric ChargeThe ancient Greeks discovered as early as 600 B.C. that after they rubbed amberwith wool, the amber could attract other objects. Today we say that the amber hasacquired a net electric charge, or has become charged. The word “electric” isderived from the Greek word elektron, meaning amber. When you scuff yourshoes across a nylon carpet, you become electrically charged, and you can chargea comb by passing it through dry hair.

Plastic rods and fur (real or fake) are particularly good for demonstratingelectrostatics, the interactions between electric charges that are at rest (or nearlyso). After we charge both plastic rods in Fig. 21.1a by rubbing them with thepiece of fur, we find that the rods repel each other.

When we rub glass rods with silk, the glass rods also become charged andrepel each other (Fig. 21.1b). But a charged plastic rod attracts a charged glassrod; furthermore, the plastic rod and the fur attract each other, and the glass rodand the silk attract each other (Fig. 21.1c).

These experiments and many others like them have shown that there areexactly two kinds of electric charge: the kind on the plastic rod rubbed with furand the kind on the glass rod rubbed with silk. Benjamin Franklin (1706–1790)suggested calling these two kinds of charge negative and positive, respectively,and these names are still used. The plastic rod and the silk have negative charge;the glass rod and the fur have positive charge.

Two positive charges or two negative charges repel each other. A positive chargeand a negative charge attract each other.

CAUTION Electric attraction and repulsion The attraction and repulsion of two chargedobjects are sometimes summarized as “Like charges repel, and opposite charges attract.”But keep in mind that the phrase “like charges” does not mean that the two charges areexactly identical, only that both charges have the same algebraic sign (both positive orboth negative). “Opposite charges” means that both objects have an electric charge, andthose charges have different signs (one positive and the other negative). ❙

688 CHAPTER 21 Electric Charge and Electric Field

++ +

+ +++++

++ + + +

PlasticFur

(a) Interaction between plastic rods rubbedon fur

– – – – –– –

–– –

... but after beingrubbed with fur,the rods repeleach other.

Plain plastic rods neither attract nor repel each other ...

Silk Glass

(b) Interaction between glass rods rubbedon silk

++ + + ++

++

+ +

... but after beingrubbed with silk,the rods repeleach other.

Plain glass rods neither attract nor repel each other ...

(c) Interaction between objects with oppositecharges

++ + + +– – – – –

... and the fur and silkeach attracts the rod it rubbed.

The fur-rubbed plasticrod and the silk-rubbed glass rod

attract eachother ...

21.1 Experiments in electrostatics. (a) Negatively charged objects repel each other. (b) Positively charged objects repel each other. (c) Positvely charged objects and negatively charged objects attract each other.

Cargas  elétricas  vêm  em  dois  “sabores”:  +  e  -­‐  (B  Franklin,  sec  XVIII).  De  mesmo  sinal  se  repelem;  de  sinais  opostos,  se  atraem

3IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

Carga  elétrica  e  estrutura  da  matéria:  átomos  são  os  Kjolos  da  matéria  

mp=mn=1,67x10-­‐27  kgme=9,1x10-­‐31  kg

aprox  99,9%  da  massa  de  um  átomo  está  

concentrada  no  núcleo

|qe|=|qp|=  e  =  1,6  x10-­‐19C  

Átomos  neutros:  No.  prótons  =  No.  elétrons

Um  “corpo”  é  composto  de  muitos  átomos:  pode  estar  carregado  posiKva  

ou  negaKvamente

Num  sistema  fechado:  soma  algébrica  de  todas  as  

cargas  é  constante

Ex:  Pele  +  bastão:  carga  é  transferida  de  um  para  o  outro

Unidade  de  carga:  e  quanKzação

IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

21.2  Condutores,  Isolantes  e  Cargas  Induzidas

Os  diversos  materiais  podem  ser  caracterizados  pela  facilidade,  ou  dificuldade,  com  que  cargas  elétricas  fluem  por  ele:•bons  condutores    -­‐  transporte  de  carga  é  fácil  (rápido,  pequena  resistência);  p.ex.,  metais•isolantes  -­‐  transporte  de  carga  muito  diicil  ou  não  permiKdo;  p.ex.,  borracha•semicondutores  -­‐  intermediários;  p.ex.,  chip  de  Si•supercondutores  -­‐  corrente  passa  sem  perdas.

Fio  de  Cu  encapado  com  borracha:  corrente  passa  internamente,  mas  a  borracha  evita  o  despejo  de  carga  no  ar  ou  em  quem  o  toca.

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Fios  de  nylon  isolantes

Bastão  plásKco  carregado

O  fio  transporta  carga:  do  bastão  carregado  à  bola  de  metal,  que,  neste  caso,  fica  carregada  negaKvamente

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Ao  aproximarmos  um  bastão  com  carga  oposta  à  da  bola,  ele  a  atrai.

Se  a  carga  no  bastão  tem  mesmo  sinal  que  a  da  bola,  ele  a  repele.

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

5

Carregamento  por  indução

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

Suporte isolante

Bola metálica

Bola metálica inicialmente descarregadaEsfera condutora: número “ilimitado” de elétrons (e-’s) livres

Most metals are good conductors, while most nonmetals are insulators. Withina solid metal such as copper, one or more outer electrons in each atom becomedetached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. Theother electrons remain bound to the positively charged nuclei, which themselvesare bound in nearly fixed positions within the material. In an insulator there areno, or very few, free electrons, and electric charge cannot move freely throughthe material. Some materials called semiconductors are intermediate in theirproperties between good conductors and good insulators.

Charging by InductionWe can charge a metal ball using a copper wire and an electrically charged plasticrod, as in Fig. 21.6a. In this process, some of the excess electrons on the rod aretransferred from it to the ball, leaving the rod with a smaller negative charge. Butthere is a different technique in which the plastic rod can give another body acharge of opposite sign without losing any of its own charge. This process iscalled charging by induction.

Figure 21.7 shows an example of charging by induction. An uncharged metalball is supported on an insulating stand (Fig. 21.7a). When you bring a negativelycharged rod near it, without actually touching it (Fig. 21.7b), the free electrons inthe metal ball are repelled by the excess electrons on the rod, and they shifttoward the right, away from the rod. They cannot escape from the ball becausethe supporting stand and the surrounding air are insulators. So we get excess neg-ative charge at the right surface of the ball and a deficiency of negative charge(that is, a net positive charge) at the left surface. These excess charges are calledinduced charges.

Not all of the free electrons move to the right surface of the ball. As soon asany induced charge develops, it exerts forces toward the left on the other freeelectrons. These electrons are repelled by the negative induced charge on theright and attracted toward the positive induced charge on the left. The systemreaches an equilibrium state in which the force toward the right on an electron,due to the charged rod, is just balanced by the force toward the left due to theinduced charge. If we remove the charged rod, the free electrons shift back to theleft, and the original neutral condition is restored.

What happens if, while the plastic rod is nearby, you touch one end of a conduct-ing wire to the right surface of the ball and the other end to the earth (Fig. 21.7c)?The earth is a conductor, and it is so large that it can act as a practically infinitesource of extra electrons or sink of unwanted electrons. Some of the negativecharge flows through the wire to the earth. Now suppose you disconnect the wire(Fig. 21.7d) and then remove the rod (Fig. 21.7e); a net positive charge is left onthe ball. The charge on the negatively charged rod has not changed during thisprocess. The earth acquires a negative charge that is equal in magnitude to theinduced positive charge remaining on the ball.

692 CHAPTER 21 Electric Charge and Electric Field

––

––

–

––– – –

––

–– + +++

+

Insulatingnylon threads

Metalball

Copperwire

Chargedplastic rod

Chargedglass rod

Charged plastic rod

The wire conducts charge from the negativelycharged plastic rod to the metal ball.

... and a positivelycharged glass rodattracts the ball.

A negatively chargedplastic rod now repelsthe ball ...

(a)

(b)

(c)

21.6 Copper is a good conductor ofelectricity; nylon is a good insulator. (a)The copper wire conducts charge betweenthe metal ball and the charged plastic rod tocharge the ball negatively. Afterward, themetal ball is (b) repelled by a negativelycharged plastic rod and (c) attracted to apositively charged glass rod.

– –

++

++

+++ –

–

–

+ –––––

+++

+ –––––––

–

– – – –

–––– +++

+

– –

Metalball

Insulatingstand

Electron buildupElectrondeficiency

Negativelychargedrod

Ground

WireNegativecharge inground

(a) Uncharged metal ball (b) Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.

(c) Wire lets electron build-up (induced negativecharge) flow intoground.

(d) Wire removed; ball nowhas only an electron-deficient region ofpositive charge.

(e) Rod removed; electrons rearrangethemselves, ball hasoverall electrondeficiency (net positive charge).

21.7 Charging a metal ball by induction.

•Conectamos a bola à Terra (é condutora e muito grande: atua como fonte de elétrons extras ou dreno de elétrons em excesso) por meio de um fio de metal. •e-’s acumulados migram para a Terra

bastão carregado negativamente

deficiência de elétrons

acúmulo de elétrons

•Aproximamos um bastão negativo; •e-’s (livres para se moverem!) se afastam do bastão;•excesso de carga positiva (deficiência de e-’s) perto do bastão.

IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

Fio removido: cargas positivas (i.e., deficiência de elétrons) permanecem na bola;

Bastão removido: cargas positivas (i.e., as cargas negativas dos elétrons) se rearrumam numa distribuição aprox. uniforme

6IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

Forças  elétricas  em  objetos  descarregados

21.3 Coulomb’s Law 693

Electric Forces on Uncharged ObjectsFinally, we note that a charged body can exert forces even on objects that arenot charged themselves. If you rub a balloon on the rug and then hold the bal-loon against the ceiling, it sticks, even though the ceiling has no net electriccharge. After you electrify a comb by running it through your hair, you can pickup uncharged bits of paper or plastic with the comb (Fig. 21.8a). How is thispossible?

This interaction is an induced-charge effect. Even in an insulator, electriccharges can shift back and forth a little when there is charge nearby. This isshown in Fig. 21.8b; the negatively charged plastic comb causes a slight shift-ing of charge within the molecules of the neutral insulator, an effect calledpolarization. The positive and negative charges in the material are present inequal amounts, but the positive charges are closer to the plastic comb and sofeel an attraction that is stronger than the repulsion felt by the negative charges,giving a net attractive force. (In Section 21.3 we will study how electric forcesdepend on distance.) Note that a neutral insulator is also attracted to a positivelycharged comb (Fig. 21.8c). Now the charges in the insulator shift in the oppo-site direction; the negative charges in the insulator are closer to the comb andfeel an attractive force that is stronger than the repulsion felt by the positivecharges in the insulator. Hence a charged object of either sign exerts an attrac-tive force on an uncharged insulator. Figure 21.9 shows an industrial applica-tion of this effect.

+++++

++++ +

++++ + +

+

–

–+–

+ –

+–+–

+–+ –

+ –+–

+ –+ –

+ –

+ –

++

Negativelycharged comb

Positivelycharged comb

As a result, the(1) charges in each

molecule are closer tothe comb than are the (2)

charges and so feel a strongerforce from the comb. Therefore

the net force is attractive.

Electrons in eachmolecule of the neutralinsulator shift awayfrom the comb.

This time, electrons inthe molecules shifttoward the comb ...

... so that the(2) charges in each

molecule are closer tothe comb, and feel a

stronger force from it, thanthe (+) charges. Again, the net

force is attractive.

+–+–

+–+–

+–

+–+–

+–

+–+–

+–+–

–––––

–––

–––––

––––

FS

FS

S2F

S2F

(a) A charged comb picking up unchargedpieces of plastic

(b) How a negatively charged comb attracts aninsulator

(c) How a positively charged comb attracts aninsulator

21.8 The charges within the molecules of an insulating material can shift slightly. As a result, a comb with either sign of chargeattracts a neutral insulator. By Newton’s third law the neutral insulator exerts an equal-magnitude attractive force on the comb.

Test Your Understanding of Section 21.2 You have two lightweight metalspheres, each hanging from an insulating nylon thread. One of the spheres has a net nega-tive charge, while the other sphere has no net charge. (a) If the spheres are close togetherbut do not touch, will they (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? (b) You now allow the two spheres to touch. Once they havetouched, will the two spheres (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? ❙

21.3 Coulomb’s LawCharles Augustin de Coulomb (1736–1806) studied the interaction forces ofcharged particles in detail in 1784. He used a torsion balance (Fig. 21.10a) simi-lar to the one used 13 years later by Cavendish to study the much weaker gravita-tional interaction, as we discussed in Section 13.1. For point charges, charged

+++

+

++

–– – –

––– –– –

Positive chargeis induced onsurface of metal.

Paint sprayer

Spray ofnegativelychargedpaint droplets

Metal objectto be painted

Ground

21.9 The electrostatic painting process(compare Figs. 21.7b and 21.7c). A metalobject to be painted is connected to the earth(“ground”), and the paint droplets are givenan electric charge as they exit the sprayernozzle. Induced charges of the oppositesign appear in the object as the dropletsapproach, just as in Fig. 21.7b, and theyattract the droplets to the surface. Thisprocess minimizes overspray from cloudsof stray paint particles and gives a particu-larly smooth finish.

ActivPhysics 11.1: Electric Force: Coulomb's LawActivPhysics 11.2: Electric Force: Superposition PrincipleActivPhysics 11.3: Electric Force:Superposition (Quantitative)

Após passar o pente no cabelo, ele atrai pequenos objetos neutros

(clima seco) Como pode?

21.3 Coulomb’s Law 693

Electric Forces on Uncharged ObjectsFinally, we note that a charged body can exert forces even on objects that arenot charged themselves. If you rub a balloon on the rug and then hold the bal-loon against the ceiling, it sticks, even though the ceiling has no net electriccharge. After you electrify a comb by running it through your hair, you can pickup uncharged bits of paper or plastic with the comb (Fig. 21.8a). How is thispossible?

This interaction is an induced-charge effect. Even in an insulator, electriccharges can shift back and forth a little when there is charge nearby. This isshown in Fig. 21.8b; the negatively charged plastic comb causes a slight shift-ing of charge within the molecules of the neutral insulator, an effect calledpolarization. The positive and negative charges in the material are present inequal amounts, but the positive charges are closer to the plastic comb and sofeel an attraction that is stronger than the repulsion felt by the negative charges,giving a net attractive force. (In Section 21.3 we will study how electric forcesdepend on distance.) Note that a neutral insulator is also attracted to a positivelycharged comb (Fig. 21.8c). Now the charges in the insulator shift in the oppo-site direction; the negative charges in the insulator are closer to the comb andfeel an attractive force that is stronger than the repulsion felt by the positivecharges in the insulator. Hence a charged object of either sign exerts an attrac-tive force on an uncharged insulator. Figure 21.9 shows an industrial applica-tion of this effect.

+++++

++++ +

++++ + +

+

–

–+–

+ –

+–+–

+–+ –

+ –+–

+ –+ –

+ –

+ –

++

Negativelycharged comb

Positivelycharged comb

As a result, the(1) charges in each

molecule are closer tothe comb than are the (2)

charges and so feel a strongerforce from the comb. Therefore

the net force is attractive.

Electrons in eachmolecule of the neutralinsulator shift awayfrom the comb.

This time, electrons inthe molecules shifttoward the comb ...

... so that the(2) charges in each

molecule are closer tothe comb, and feel a

stronger force from it, thanthe (+) charges. Again, the net

force is attractive.

+–+–

+–+–

+–

+–+–

+–

+–+–

+–+–

–––––

–––

–––––

––––

FS

FS

S2F

S2F

(a) A charged comb picking up unchargedpieces of plastic

(b) How a negatively charged comb attracts aninsulator

(c) How a positively charged comb attracts aninsulator

21.8 The charges within the molecules of an insulating material can shift slightly. As a result, a comb with either sign of chargeattracts a neutral insulator. By Newton’s third law the neutral insulator exerts an equal-magnitude attractive force on the comb.

Test Your Understanding of Section 21.2 You have two lightweight metalspheres, each hanging from an insulating nylon thread. One of the spheres has a net nega-tive charge, while the other sphere has no net charge. (a) If the spheres are close togetherbut do not touch, will they (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? (b) You now allow the two spheres to touch. Once they havetouched, will the two spheres (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? ❙

21.3 Coulomb’s LawCharles Augustin de Coulomb (1736–1806) studied the interaction forces ofcharged particles in detail in 1784. He used a torsion balance (Fig. 21.10a) simi-lar to the one used 13 years later by Cavendish to study the much weaker gravita-tional interaction, as we discussed in Section 13.1. For point charges, charged

+++

+

++

–– – –

––– –– –

Positive chargeis induced onsurface of metal.

Paint sprayer

Spray ofnegativelychargedpaint droplets

Metal objectto be painted

Ground

21.9 The electrostatic painting process(compare Figs. 21.7b and 21.7c). A metalobject to be painted is connected to the earth(“ground”), and the paint droplets are givenan electric charge as they exit the sprayernozzle. Induced charges of the oppositesign appear in the object as the dropletsapproach, just as in Fig. 21.7b, and theyattract the droplets to the surface. Thisprocess minimizes overspray from cloudsof stray paint particles and gives a particu-larly smooth finish.

ActivPhysics 11.1: Electric Force: Coulomb's LawActivPhysics 11.2: Electric Force: Superposition PrincipleActivPhysics 11.3: Electric Force:Superposition (Quantitative)

21.3 Coulomb’s Law 693

Electric Forces on Uncharged ObjectsFinally, we note that a charged body can exert forces even on objects that arenot charged themselves. If you rub a balloon on the rug and then hold the bal-loon against the ceiling, it sticks, even though the ceiling has no net electriccharge. After you electrify a comb by running it through your hair, you can pickup uncharged bits of paper or plastic with the comb (Fig. 21.8a). How is thispossible?

This interaction is an induced-charge effect. Even in an insulator, electriccharges can shift back and forth a little when there is charge nearby. This isshown in Fig. 21.8b; the negatively charged plastic comb causes a slight shift-ing of charge within the molecules of the neutral insulator, an effect calledpolarization. The positive and negative charges in the material are present inequal amounts, but the positive charges are closer to the plastic comb and sofeel an attraction that is stronger than the repulsion felt by the negative charges,giving a net attractive force. (In Section 21.3 we will study how electric forcesdepend on distance.) Note that a neutral insulator is also attracted to a positivelycharged comb (Fig. 21.8c). Now the charges in the insulator shift in the oppo-site direction; the negative charges in the insulator are closer to the comb andfeel an attractive force that is stronger than the repulsion felt by the positivecharges in the insulator. Hence a charged object of either sign exerts an attrac-tive force on an uncharged insulator. Figure 21.9 shows an industrial applica-tion of this effect.

+++++

++++ +

++++ + +

+

–

–+–

+ –

+–+–

+–+ –

+ –+–

+ –+ –

+ –

+ –

++

Negativelycharged comb

Positivelycharged comb

As a result, the(1) charges in each

molecule are closer tothe comb than are the (2)

charges and so feel a strongerforce from the comb. Therefore

the net force is attractive.

Electrons in eachmolecule of the neutralinsulator shift awayfrom the comb.

This time, electrons inthe molecules shifttoward the comb ...

... so that the(2) charges in each

molecule are closer tothe comb, and feel a

stronger force from it, thanthe (+) charges. Again, the net

force is attractive.

+–+–

+–+–

+–

+–+–

+–

+–+–

+–+–

–––––

–––

–––––

––––

FS

FS

S2F

S2F

(a) A charged comb picking up unchargedpieces of plastic

(b) How a negatively charged comb attracts aninsulator

(c) How a positively charged comb attracts aninsulator

21.8 The charges within the molecules of an insulating material can shift slightly. As a result, a comb with either sign of chargeattracts a neutral insulator. By Newton’s third law the neutral insulator exerts an equal-magnitude attractive force on the comb.

Test Your Understanding of Section 21.2 You have two lightweight metalspheres, each hanging from an insulating nylon thread. One of the spheres has a net nega-tive charge, while the other sphere has no net charge. (a) If the spheres are close togetherbut do not touch, will they (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? (b) You now allow the two spheres to touch. Once they havetouched, will the two spheres (i) attract each other, (ii) repel each other, or (iii) exert noforce on each other? ❙

21.3 Coulomb’s LawCharles Augustin de Coulomb (1736–1806) studied the interaction forces ofcharged particles in detail in 1784. He used a torsion balance (Fig. 21.10a) simi-lar to the one used 13 years later by Cavendish to study the much weaker gravita-tional interaction, as we discussed in Section 13.1. For point charges, charged

+++

+

++

–– – –

––– –– –

Positive chargeis induced onsurface of metal.

Paint sprayer

Spray ofnegativelychargedpaint droplets

Metal objectto be painted

Ground

21.9 The electrostatic painting process(compare Figs. 21.7b and 21.7c). A metalobject to be painted is connected to the earth(“ground”), and the paint droplets are givenan electric charge as they exit the sprayernozzle. Induced charges of the oppositesign appear in the object as the dropletsapproach, just as in Fig. 21.7b, and theyattract the droplets to the surface. Thisprocess minimizes overspray from cloudsof stray paint particles and gives a particu-larly smooth finish.

ActivPhysics 11.1: Electric Force: Coulomb's LawActivPhysics 11.2: Electric Force: Superposition PrincipleActivPhysics 11.3: Electric Force:Superposition (Quantitative)

Mesmo em isolantes, há separação de cargas (induzidas) quando em presença de carga externa, mas de um modo diferente de um metal

Um  isolante  se  polariza  em  presença  de  cargas  externas  a  ele

hnp://cnx.org/content/m42333/latest/Figure_20_05_06(a)a.jpg

21.3  A  Lei  de  Coulomb

Charles Augustin de Coulomb1736-1806

I. AULA # 2 - CAP. 1: CARGA E CAMPO ELETRICOS

F ≡ F = kq1q2r2

r

Another length scale: mean-free path, ℓ

Delocalized regime (Ohmic):

Small randomness [weak scattering, (kF ℓ)−1 ≪ 1]: σ ≈ ne2ℓ/!kF

Ohm’s law for a (d-dimensional) hypercube of size L:

g(L) = σLd−2 =⇒ g ↑ as L ↑, for d > 2

Localized regime:

Hopping between states of nearly the same energy, far apart in space:

=⇒ hopping matrix elements exponentially small

=⇒ g(L) ∝ exp(−L/ξ)

2

experiências com balança de torção estabeleceram que

I. AULA # 2 - CAP. 1: CARGA E CAMPO ELETRICOS

F ≡ F = kq1q2r2

r

Another length scale: mean-free path, ℓ

Delocalized regime (Ohmic):

Small randomness [weak scattering, (kF ℓ)−1 ≪ 1]: σ ≈ ne2ℓ/!kF

Ohm’s law for a (d-dimensional) hypercube of size L:

g(L) = σLd−2 =⇒ g ↑ as L ↑, for d > 2

Localized regime:

Hopping between states of nearly the same energy, far apart in space:

=⇒ hopping matrix elements exponentially small

=⇒ g(L) ∝ exp(−L/ξ)

2

Lei de Coulomb

Obs: 1. Note a convenção para vetor: negrito ou seta, esta mais adequada à escrita manual; note tb o vetor unitário da direção radial.2. Lei de Coulomb válida para 2 cargas puntiformes (i.e., r » dimensões típicas dos objetos carregados) 3. Força entre duas cargas de 1C, separadas por 1 m: F ∼ 1010 N

⇒ Escala de cargas apropriada é µC ≡ 10-6 C ou nC ≡ 10-9 C4.Carga do elétron e = 1,6 × 10-19 C ⇒ a carga eletrônica total em moeda de cobre é Q ∼ 105 C5. Com ε0 esta é a Lei de Coulomb no vácuo; deve ser modificada em meios materiais; vale aprox. no ar

I. AULA # 2 - CAP. 1: CARGA E CAMPO ELETRICOS

F ≡ F = kq1q2r2

r

k ≡1

4πϵ0; ϵ0 = 8, 854× 10−12 C2/N ·m2 → permissividade eletrica do vacuo

Another length scale: mean-free path, ℓ

Delocalized regime (Ohmic):

Small randomness [weak scattering, (kF ℓ)−1 ≪ 1]: σ ≈ ne2ℓ/!kF

Ohm’s law for a (d-dimensional) hypercube of size L:

g(L) = σLd−2 =⇒ g ↑ as L ↑, for d > 2

Localized regime:

Hopping between states of nearly the same energy, far apart in space:

=⇒ hopping matrix elements exponentially small

=⇒ g(L) ∝ exp(−L/ξ)

2

[q] = C(Coulomb)

permissividade elétrica do vácuo

k ≈ 9,0 × 109 N⋅m2/C2

IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

I. AULA # 2 - CAP. 1: CARGA E CAMPO ELETRICOS

F ≡ F = kq1q2r2

r

Another length scale: mean-free path, ℓ

Delocalized regime (Ohmic):

Small randomness [weak scattering, (kF ℓ)−1 ≪ 1]: σ ≈ ne2ℓ/!kF

Ohm’s law for a (d-dimensional) hypercube of size L:

g(L) = σLd−2 =⇒ g ↑ as L ↑, for d > 2

Localized regime:

Hopping between states of nearly the same energy, far apart in space:

=⇒ hopping matrix elements exponentially small

=⇒ g(L) ∝ exp(−L/ξ)

2

Lei de Coulomb

Linear em q1 e q2 ⇒ vale superposição

q1

qT

q2FR

F2F1

Exemplo: qual a força resultante em Q?

IF/UFRJ - Física III - 2014/1 - Prof. Raimundo Rocha dos Santos - Cap. 1 - Carga e campo elétricos - Aula No. 1

i.e., a força resultante devido a várias cargas fixas é a soma vetorial das forças que cada uma faria, se as demais não estivessem presentes.

(solução no quadro)