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Physics II

IntroductionIntroduction

Electricity and Magnetism• Properties of electric charges• Insulators and conductors• Coulomb’s law

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IntroductionIntroduction

Knowledge of electricity dates back to Greek antiquity Knowledge of electricity dates back to Greek antiquity (700 BC).(700 BC).Began with the realization that amber (fossil) when Began with the realization that amber (fossil) when rubbed with wool, attracts small objects.rubbed with wool, attracts small objects.This phenomenon is not restricted to amber/wool but may This phenomenon is not restricted to amber/wool but may occur whenever two nonoccur whenever two non--conducting substances are conducting substances are rubbed together.rubbed together.

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11.. Properties of Electric Charges Properties of Electric Charges -- DiscoveryDiscovery

Observation of Observation of ““Static ElectricityStatic Electricity””A comb passed though hair attracts small pieces of paper.A comb passed though hair attracts small pieces of paper.An inflated balloon rubbed with wool.An inflated balloon rubbed with wool.

““Electrically chargedElectrically charged””Rub shoes against carpet/car seat to charge your body.Rub shoes against carpet/car seat to charge your body.Remove this charge by touching another person/a piece of Remove this charge by touching another person/a piece of metal.metal.

Two kinds of chargesTwo kinds of chargesNamed by Benjamin Franklin (1706Named by Benjamin Franklin (1706--1790) as 1790) as positivepositive and and negativenegative..

Like charges repel one another and unlike charges Like charges repel one another and unlike charges attract one anotherattract one another..

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11.. Properties of Electric ChargesProperties of Electric ChargesNature of Electrical ChargeNature of Electrical Charge

Origin of charge is at the atomic level.Origin of charge is at the atomic level.Nucleus : Nucleus : ““robustrobust””, , positivepositive..Electrons : mobile, Electrons : mobile, negativenegative..

Usual state of the atom is Usual state of the atom is neutralneutral..Charge has natural tendency to be transferred between Charge has natural tendency to be transferred between unlike materials.unlike materials.Electric charge is however always Electric charge is however always conservedconserved in the in the process.process.

Charge is Charge is not creatednot created..Usually, Usually, negative chargenegative charge is transferred from one object to the is transferred from one object to the other.other.

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11.. Properties of Electric ChargesProperties of Electric ChargesQuantizationQuantization

Robert Robert MillikanMillikan found, in 1909, that charged objects may only have found, in 1909, that charged objects may only have an integer multiple of a fundamental unit of charge.an integer multiple of a fundamental unit of charge.

Charge is Charge is quantizedquantized..An object may have a charge An object may have a charge ±±e, or e, or ±± 2e, or 2e, or ±± 3e, etc but not say 3e, etc but not say ±±1.5e.1.5e.Proton has a charge Proton has a charge +1e+1e..Electron has a charge Electron has a charge ––1e1e..Some particles such a Some particles such a neutronneutron have no (zero) charge.have no (zero) charge.A neutral atom has as many positive and negative charges.A neutral atom has as many positive and negative charges.

UnitsUnitsIn SI, electrical charge is measured in coulomb ( C).In SI, electrical charge is measured in coulomb ( C).The value of |The value of |e| = 1.602 x 10e| = 1.602 x 10--1919 CC..

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22.. Insulators and Conductors Insulators and Conductors ––Material Material classificationclassification

Materials/substances may be classified according to their capaciMaterials/substances may be classified according to their capacity to ty to carry or carry or conductconduct electric charge electric charge ConductorsConductors are material in which electric charges move freely.are material in which electric charges move freely.Insulator Insulator are materials in which electrical charge do not move freely.are materials in which electrical charge do not move freely.

Glass, Rubber are good insulators.Glass, Rubber are good insulators.Copper, aluminum, and silver are good conductors.Copper, aluminum, and silver are good conductors.

Semiconductors are a third class of materials with electrical Semiconductors are a third class of materials with electrical properties somewhere between those of insulators and conductors.properties somewhere between those of insulators and conductors.

Silicon and germanium are semiconductors used widely in the Silicon and germanium are semiconductors used widely in the fabrication of electronic devices.fabrication of electronic devices.

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MiniMini--quiz:quiz:

Identify substances or materials that can be classified asIdentify substances or materials that can be classified asConductors ?Conductors ?Insulators?Insulators?

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22.. Insulators and Conductors Insulators and Conductors –– Charging by Charging by Conduction.Conduction.

Consider negatively charge rubber rod brought into contact Consider negatively charge rubber rod brought into contact with a neutral conducting but insulated sphere.with a neutral conducting but insulated sphere.Some electrons located on the rubber move to the sphere.Some electrons located on the rubber move to the sphere.Remove the rubber rod.Remove the rubber rod.Excess electrons left on the sphere. It is Excess electrons left on the sphere. It is negatively chargednegatively charged..This process is referred as This process is referred as charging by conductioncharging by conduction..

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22.. Insulators and Conductors Insulators and Conductors –– Earth/Ground.Earth/Ground.

When a conductor is connected to Earth with a When a conductor is connected to Earth with a conducting wire or pipe, it is said to be conducting wire or pipe, it is said to be groundedgrounded..Earth provides a Earth provides a quasi infinite reservoirquasi infinite reservoir of electrons: can of electrons: can accept or supply an unlimited number of electrons.accept or supply an unlimited number of electrons.

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22.. Insulators and Conductors Insulators and Conductors –– Charging by Charging by Induction.Induction.

Consider a negatively charged rubber rod brought Consider a negatively charged rubber rod brought nearnear a neutral a neutral conducting sphere insulated from the ground.conducting sphere insulated from the ground.Repulsive force between electrons causes redistribution of chargRepulsive force between electrons causes redistribution of charges on es on the sphere.the sphere.Electrons move away from the rod leaving an excess of positive Electrons move away from the rod leaving an excess of positive charges near the rod. charges near the rod. Connect a wire between sphere and Earth on the far side of the Connect a wire between sphere and Earth on the far side of the sphere.sphere.Repulsion between electrons cause electrons to move from sphere Repulsion between electrons cause electrons to move from sphere to to Earth.Earth.Disconnect the wire.Disconnect the wire.The sphere now has a positive net charge.The sphere now has a positive net charge.This process is referred as This process is referred as charging by inductioncharging by induction..Charging by induction requires no contact with the object induciCharging by induction requires no contact with the object inducing the ng the charge.charge.

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22.. Insulators and Conductors Insulators and Conductors –– Charging by Charging by Induction.Induction.Consider a negatively charged rubber rod Consider a negatively charged rubber rod brought brought nearnear a neutral conducting sphere a neutral conducting sphere insulated from the ground.insulated from the ground.Repulsive force between electrons causes Repulsive force between electrons causes redistribution of charges on the sphere.redistribution of charges on the sphere.Electrons move away from the rod leaving an Electrons move away from the rod leaving an excess of positive charges near the rod. excess of positive charges near the rod. Connect a wire between sphere and Earth on Connect a wire between sphere and Earth on the far side of the sphere.the far side of the sphere.Repulsion between electrons cause electrons Repulsion between electrons cause electrons to move from sphere to Earth.to move from sphere to Earth.Disconnect the wire.Disconnect the wire.The sphere now has a positive net charge.The sphere now has a positive net charge.This process is referred as This process is referred as charging by charging by inductioninduction..Charging by induction requires no contact Charging by induction requires no contact with the object inducing the charge.with the object inducing the charge.

Q: How does this mechanism work is we bring is a positively charged glass rod instead?

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22.. Insulators and Conductors Insulators and Conductors –– Polarization.Polarization.

Polarization is realignment of charge within individual Polarization is realignment of charge within individual molecules.molecules.Produces induced charge on the surface of insulators.Produces induced charge on the surface of insulators.how e.g. rubber or glass can be used to supply how e.g. rubber or glass can be used to supply electrons.electrons.

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MiniMini--quizquizA positively charged object hanging from a string is brought neaA positively charged object hanging from a string is brought near a non r a non conducting object (ball). The ball is seen to be attracted to thconducting object (ball). The ball is seen to be attracted to the object. e object.

1.1.Explain why it is not possible to determine whether the object iExplain why it is not possible to determine whether the object is s negatively charged or neutral.negatively charged or neutral.2.2.What additional experiment is needed to reveal the electrical chWhat additional experiment is needed to reveal the electrical charge arge state of the object?state of the object?

? +

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Explain why it is not possible to determine whether Explain why it is not possible to determine whether the object is negatively charged or neutral.the object is negatively charged or neutral.

Two possibilities: Two possibilities: Attraction between objects of unlike charges.Attraction between objects of unlike charges.

Attraction between a charged object and a neutral object subjectAttraction between a charged object and a neutral object subjectto polarization.to polarization.

- +

+----

++

++

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What additional experiment is needed to reveal the What additional experiment is needed to reveal the electrical charge state of the object?electrical charge state of the object?

Two Experiments:Two Experiments:Bring known neutral ball near the object and observe whether theBring known neutral ball near the object and observe whether there is re is an attraction.an attraction.

Bring a known negatively charge object near the first one. If thBring a known negatively charge object near the first one. If there is an ere is an attraction, the object is neutral, and the attraction is achieveattraction, the object is neutral, and the attraction is achieved by d by polarization.polarization.

? 0

-++++

+--+-

+-

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33.. CoulombCoulomb’’s Law s Law -- ObservationObservation

Charles Coulomb discovered in 1785 the fundamental law of Charles Coulomb discovered in 1785 the fundamental law of electrical force between two stationary charged particles.electrical force between two stationary charged particles.An electric force has the following properties:An electric force has the following properties:

Inversely proportional to the square of the separation, r, betweInversely proportional to the square of the separation, r, between the en the particles, and is along a line joining them.particles, and is along a line joining them.Proportional to the product of the magnitudes of the charges |qProportional to the product of the magnitudes of the charges |q11| and | and |q|q22| on the two particles. | on the two particles. Attractive if the charges are of opposite sign and repulsive if Attractive if the charges are of opposite sign and repulsive if the charges the charges have the same sign.have the same sign.

q1 q2

r

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33.. CoulombCoulomb’’s Law s Law –– Mathematical Mathematical FormulationFormulation

kkee known as the Coulomb constant.known as the Coulomb constant.Value of Value of kkee depends on the choice of units.depends on the choice of units.SI unitsSI units

Force: the Newton (N)Force: the Newton (N)Charge: the coulomb ( C).Charge: the coulomb ( C).Current: the ampere (A =1 C/s).Current: the ampere (A =1 C/s).Distance: the meter (m).Distance: the meter (m).

EExperimentally measurement: xperimentally measurement: kkee = 8.9875= 8.9875××101099 NmNm22/C/C22..Reasonable approximate value: Reasonable approximate value: kkee = 8.99= 8.99××101099 NmNm22/C/C22..

1 22e

q qF k

r=

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Charge and Mass of the Electron, Proton Charge and Mass of the Electron, Proton and Neutron.and Neutron.

1.67 1.67 ××1010--272700NeutronNeutron

1.67 1.67 ××1010--2727+1.60 +1.60 ××1010--1919ProtonProton

9.11 9.11 ××1010--3131--1.60 1.60 ××1010--1919ElectronElectron

Mass (kg)Mass (kg)Charge ( C)Charge ( C)ParticleParticle

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ExampleExample

1e = 1e = --1.60 1.60 ××1010--1919 ccTakes 1/e=6.6 Takes 1/e=6.6 ××10101818 protons to create a total charge of 1Cprotons to create a total charge of 1CNumber of free electrons in 1 cmNumber of free electrons in 1 cm33 copper ~ 10copper ~ 102323

Charge obtained in typical electrostatic experiments with Charge obtained in typical electrostatic experiments with rubber or glass 10rubber or glass 10--66 C = 1 C = 1 μμccA very small fraction of the total available chargeA very small fraction of the total available charge

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33.. CoulombCoulomb’’s Law s Law –– RemarksRemarks

The electrostatic force is often called Coulomb force.The electrostatic force is often called Coulomb force.It is a force: It is a force:

a magnitude a magnitude a direction.a direction.

Second example of action at a distance.Second example of action at a distance.

++

r

q1q2

F21

F21 +-

r

q1

q2F21F21

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MiniMini--QuizQuiz

Name the first action at a distance force you have Name the first action at a distance force you have encountered in physics so far.encountered in physics so far.

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Example: Electrical ForceExample: Electrical Force

Question:Question:The electron and proton of a hydrogen atom are separated (on theThe electron and proton of a hydrogen atom are separated (on theaverage) by a distance of about 5.3x10average) by a distance of about 5.3x10--1111 m. Find the magnitude of the m. Find the magnitude of the electric force that each particle exerts on the other.electric force that each particle exerts on the other.

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Question:Question:The electron and proton of a hydrogen atom are separated (on theThe electron and proton of a hydrogen atom are separated (on the average) by average) by

a distance of about 5.3x10a distance of about 5.3x10--1111 m. Find the magnitude of the electric force that m. Find the magnitude of the electric force that each particle exerts on the other.each particle exerts on the other.

1 22e

q qF k

r=

Observations:Observations:We are interested in finding the magnitude of the force between We are interested in finding the magnitude of the force between two two particles of known charge, and a given distance of each other.particles of known charge, and a given distance of each other.The magnitude is given by CoulombThe magnitude is given by Coulomb’’s law.s law.

qq11 ==--1.60x101.60x10--1919 CCqq22 =1.60x10=1.60x10--1919 CCr = 5.3x10r = 5.3x10+11+11 mm

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Question:Question:The electron and proton of a hydrogen atom are separated (on theThe electron and proton of a hydrogen atom are separated (on the average) by average) by a distance of about 5.3x10a distance of about 5.3x10--1111 m. Find the magnitude of the electric force that m. Find the magnitude of the electric force that each particle exerts on the other.each particle exerts on the other.

Observations:Observations:We are interested in finding the magnitude of the force between We are interested in finding the magnitude of the force between two two particles of known charge, and a given distance of each other.particles of known charge, and a given distance of each other.The magnitude is given by CoulombThe magnitude is given by Coulomb’’s law.s law.qq11 ==--1.60x101.60x10--1919 CCqq22 =1.60x10=1.60x10--1919 CCr = 5.3x10r = 5.3x10--1111 mm

Solution:Solution:

Attractive force with a magnitude of 8.2x10Attractive force with a magnitude of 8.2x10--88 N.N.

( )( )

2

2

22 199 8

22 11

1.6 108.99 10 8.2 10

5.3 10Nm

e e C

CeF k N

r m

−−

−

×= = × = ×

×

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Superposition PrincipleSuperposition Principle

From observations: one finds that whenever multiple From observations: one finds that whenever multiple charges are present, the net force on a given charge is charges are present, the net force on a given charge is the the vectorvector sum of all forces exerted by other charges.sum of all forces exerted by other charges.Electric force obeys a Electric force obeys a superposition principlesuperposition principle..

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Example: Using the Superposition PrincipleExample: Using the Superposition Principle

Consider three point charges at the corners of a triangle, as shConsider three point charges at the corners of a triangle, as shown own below. Find the resultant force on qbelow. Find the resultant force on q33 if if qq11 = 6.00 x 10= 6.00 x 10--99 CCqq2 2 = = --2.00 x 102.00 x 10--99 CCqq3 3 = 5.00 x 10= 5.00 x 10--99 CC

+ x

y

- +q2

q1

3.00 m

4.00 mq3

F32

F31

37.0o

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Consider three point charges at the corners of a triangle, as shConsider three point charges at the corners of a triangle, as shown own below. Find the resultant force on qbelow. Find the resultant force on q33..

Observations:Observations:The superposition principle tells us that the net force on qThe superposition principle tells us that the net force on q33 is the vector sum is the vector sum of the forces Fof the forces F3232 and Fand F3131..The magnitude of the forces FThe magnitude of the forces F3232 and Fand F3131 can calculated using Coulombcan calculated using Coulomb’’s s law.law.

+ x

y

- +q2

q1

3.00 m

4.00 mq3

F32

F31

37.0o

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Consider three point charges at the corners of a triangle, as shConsider three point charges at the corners of a triangle, as shown own below. Find the resultant force on qbelow. Find the resultant force on q33..

5.00 m

( )( )( )

( )( )( )

2

2

2

2

9 93 2 9 9

32 22

9 93 1 9 8

31 22

932 31

931

2 2 9

5.00 10 2.00 108.99 10 5.62 10

4.00

5.00 10 6.00 108.99 10 1.08 10

5.00

cos37.0 3.01 10

sin 37.0 6.50 10

7.16 10

Nme C

Nme C

ox

oy

x y

C Cq qF k N

r m

C Cq qF k N

r m

F F F N

F F N

F F F N

− −−

− −−

−

−

−

× ×= = × = ×

× ×= = × = ×

= + = ×

= = ×

= + = ×

65.2oθ =

Solution:Solution:

+ x

y- +q2

q1

3.00 m4.00 m

q3

F32

F31

37.0o