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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)
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