Chapter 18Chapter 18

Electricity at RestElectricity at Rest

A Bit of HistoryA Bit of History

Ancient GreeksAncient Greeks• Observed electric and magnetic Observed electric and magnetic

phenomena as early as 700 BCphenomena as early as 700 BC Found that amber, when rubbed, became Found that amber, when rubbed, became

electrified and attracted pieces of straw or electrified and attracted pieces of straw or feathersfeathers

Magnetic forces were discovered by Magnetic forces were discovered by observing magnetite attracting ironobserving magnetite attracting iron

A Bit More HistoryA Bit More History

William GilbertWilliam Gilbert• 16001600• Found that electrification was not Found that electrification was not

limited to amberlimited to amber Charles CoulombCharles Coulomb

• 17851785• Confirmed the inverse square Confirmed the inverse square

relationship of electrical forcesrelationship of electrical forces

Electrostatics: Study of charges at restElectrostatics: Study of charges at rest

More Properties of ChargeMore Properties of Charge

Nature’s basic carrier of negative Nature’s basic carrier of negative charge is the electroncharge is the electron• Gaining or losing electrons is how an Gaining or losing electrons is how an

object becomes chargedobject becomes charged Electric charge is always conservedElectric charge is always conserved

• Charge is not created, only exchangedCharge is not created, only exchanged• Objects become charged because Objects become charged because

negative charge is transferred from one negative charge is transferred from one object to anotherobject to another

Properties of Charge, finalProperties of Charge, final

Charge is quantizedCharge is quantized• All charge is a multiple of a fundamental All charge is a multiple of a fundamental

unit of charge, symbolized by eunit of charge, symbolized by e Quarks are the exceptionQuarks are the exception

• Electrons have a charge of –eElectrons have a charge of –e• Protons have a charge of +eProtons have a charge of +e• The SI unit of charge is the Coulomb (C)The SI unit of charge is the Coulomb (C)

e = 1.6 x 10e = 1.6 x 10-19-19 C C

ConductorsConductors

Conductors are materials in which Conductors are materials in which the electric charges move freelythe electric charges move freely• Copper, aluminum and silver are good Copper, aluminum and silver are good

conductorsconductors• When a conductor is charged in a small When a conductor is charged in a small

region, the charge readily distributes region, the charge readily distributes itself over the entire surface of the itself over the entire surface of the materialmaterial

InsulatorsInsulators

Insulators are materials in which Insulators are materials in which electric charges do not move freelyelectric charges do not move freely• Glass and rubber are examples of Glass and rubber are examples of

insulatorsinsulators• When insulators are charged by rubbing, When insulators are charged by rubbing,

only the rubbed area becomes chargedonly the rubbed area becomes charged There is no tendency for the charge to move There is no tendency for the charge to move

into other regions of the materialinto other regions of the material

SemiconductorsSemiconductors

The characteristics of The characteristics of semiconductors are between those of semiconductors are between those of insulators and conductorsinsulators and conductors

Silicon and germanium are examples Silicon and germanium are examples of semiconductorsof semiconductors

Charging by ConductionCharging by Conduction A charged object (the rod) A charged object (the rod)

is placed in contact with is placed in contact with another object (the another object (the sphere)sphere)

Some electrons on the rod Some electrons on the rod can move to the spherecan move to the sphere

When the rod is removed, When the rod is removed, the sphere is left with a the sphere is left with a chargecharge

The object being charged The object being charged is always left with a charge is always left with a charge having the same sign as having the same sign as the object doing the the object doing the chargingcharging

Charging by InductionCharging by Induction When an object is When an object is

connected to a conducting connected to a conducting wire or pipe buried in the wire or pipe buried in the earth, it is said to be earth, it is said to be groundedgrounded

A negatively charged A negatively charged rubber rod is brought near rubber rod is brought near an uncharged spherean uncharged sphere

The charges in the sphere The charges in the sphere are redistributedare redistributed• Some of the electrons in Some of the electrons in

the sphere are repelled the sphere are repelled from the electrons in the from the electrons in the rodrod

Charging by Induction, contCharging by Induction, cont

The region of the sphere nearest the The region of the sphere nearest the negatively charged rod has an negatively charged rod has an excess of positive charge because of excess of positive charge because of the migration of electrons away from the migration of electrons away from this locationthis location

A grounded conducting wire is A grounded conducting wire is connected to the sphereconnected to the sphere• Allows some of the electrons to move Allows some of the electrons to move

from the sphere to the groundfrom the sphere to the ground

Charging by Induction, finalCharging by Induction, final

The wire to ground is removed, the The wire to ground is removed, the sphere is left with an excess of induced sphere is left with an excess of induced positive chargepositive charge

The positive charge on the sphere is The positive charge on the sphere is evenly distributed due to the repulsion evenly distributed due to the repulsion between the positive chargesbetween the positive charges

Charging by induction requires no Charging by induction requires no contact with the object inducing the contact with the object inducing the chargecharge

Coulomb’s LawCoulomb’s Law

Coulomb shows that an electrical force Coulomb shows that an electrical force has the following properties:has the following properties:• It is inversely proportional to the square of It is inversely proportional to the square of

the separation between the two particles the separation between the two particles and is along the line joining themand is along the line joining them

• It is proportional to the product of the It is proportional to the product of the magnitudes of the charges Qmagnitudes of the charges Q11 and Q and Q22 on the on the two particlestwo particles

• It is attractive if the charges are of opposite It is attractive if the charges are of opposite signs and repulsive if the charges have the signs and repulsive if the charges have the same signssame signs

Coulomb’s Law, cont.Coulomb’s Law, cont.

Mathematically,Mathematically,

k is called the k is called the Coulomb ConstantCoulomb Constant• k = 8.99 x 10k = 8.99 x 1099 N m N m22/C/C22

Typical charges can be in the µC rangeTypical charges can be in the µC range• Remember, Coulombs must be used in the Remember, Coulombs must be used in the

equationequation Remember that force is a Remember that force is a vector vector quantityquantity

221

r

QQkF

Coulomb’s LawCoulomb’s Law

Coulomb’s lawCoulomb’s law

2r

QqkFE

q Q

More than two charges? SUPERPOSE them!!!

...321 FFFF

Electrical FieldElectrical Field

Maxwell developed an approach to Maxwell developed an approach to discussing fieldsdiscussing fields

An An electric fieldelectric field is said to exist in the is said to exist in the region of space around a charged region of space around a charged objectobject• When another charged object enters this When another charged object enters this

electric field, the field exerts a electric field, the field exerts a forceforce on on the second charged objectthe second charged object

Electric Field, EElectric Field, E

Force on a positive unit charge (N/C).Force on a positive unit charge (N/C).Therefore, E-field superposable!!!Therefore, E-field superposable!!!

If there is E-field, there is force!!!If there is E-field, there is force!!!• ((++)-charge feels force // E-field)-charge feels force // E-field• (-)-charge feels opposite to E-field.(-)-charge feels opposite to E-field.

qE F E

This does not mean the positive (negative) charge will follow the E-field line.

Electric Field of Point ChargeElectric Field of Point Charge

Electric field at distance r from a Electric field at distance r from a point charge Q ispoint charge Q is

Electric field from many charges: Electric field from many charges: superposition (vector sum)superposition (vector sum)

2r

QkE

...321 EEEE

Direction of Electric FieldDirection of Electric Field

The electric field The electric field produced by a produced by a positive charge is positive charge is directed away directed away from the chargefrom the charge• A positive unit A positive unit

charge would be charge would be repelled from the repelled from the positive source positive source chargecharge

Direction of Electric Field, ContDirection of Electric Field, Cont

The electric field The electric field produced by a produced by a negative charge negative charge is directed toward is directed toward the chargethe charge• A positive unit A positive unit

charge would be charge would be attracted to the attracted to the negative source negative source chargecharge

Electric Field LinesElectric Field Lines

A convenient aid for visualizing A convenient aid for visualizing electric field patterns is to draw lines electric field patterns is to draw lines pointing in the direction of the field pointing in the direction of the field vector at any pointvector at any point

These are called These are called electric field lineselectric field lines and were introduced by Michael and were introduced by Michael FaradayFaraday

Electric Field Lines, cont.Electric Field Lines, cont.

The field lines are related to the field The field lines are related to the field byby• The electric field vector, E, is tangent to The electric field vector, E, is tangent to

the electric field lines at each pointthe electric field lines at each point• The number of lines per unit area The number of lines per unit area

through a surface perpendicular to the through a surface perpendicular to the lines is proportional to the strength of lines is proportional to the strength of the electric field in a given regionthe electric field in a given region

Electric Field Line PatternsElectric Field Line Patterns

Point chargePoint charge The lines radiate The lines radiate

equally in all equally in all directionsdirections

For a positive For a positive source charge, the source charge, the lines will radiate lines will radiate outwardoutward

Electric Field Line PatternsElectric Field Line Patterns

For a negative For a negative source charge, the source charge, the lines will point lines will point inwardinward

Electric Field Line PatternsElectric Field Line Patterns

An electric An electric dipoledipole consists of two consists of two equal and opposite equal and opposite chargescharges

The high density of The high density of lines between the lines between the charges indicates charges indicates the strong electric the strong electric field in this regionfield in this region

Electric Field Line PatternsElectric Field Line Patterns Two equal but like point Two equal but like point

charges charges At a great distance from At a great distance from

the charges, the field the charges, the field would be approximately would be approximately that of a single charge of that of a single charge of 2q2q

The bulging out of the field The bulging out of the field lines between the charges lines between the charges indicates the repulsion indicates the repulsion between the chargesbetween the charges

The low field lines between The low field lines between the charges indicates a the charges indicates a weak field in this regionweak field in this region

Electric Field PatternsElectric Field Patterns

Unequal and unlike Unequal and unlike chargescharges

Note that two lines Note that two lines leave the +2q leave the +2q charge for each charge for each line that line that terminates on -qterminates on -q

Uniform Electric Field between Uniform Electric Field between Parallel Charged PlatesParallel Charged Plates

Constant force on a charged Constant force on a charged particleparticle

ExampleExample

Determine electric field 30 cm from a Determine electric field 30 cm from a 55C point chargeC point charge

ExampleExample

Determine the force on an electron Determine the force on an electron between two parallel plates. between two parallel plates.

(E=6 x 10(E=6 x 1044 N/C) N/C)

ExampleExample

More electrostatic problemsMore electrostatic problems

Potential—Potential DifferencePotential—Potential Difference

Potential at a point away from a Potential at a point away from a point charge Qpoint charge Q

Work done to move an unit charge Work done to move an unit charge from infinity to point Pfrom infinity to point P

Q positive, positive workQ positive, positive work Q negative, negative work Q negative, negative work Many point charges --- superpositionMany point charges --- superposition

r

QkVp J/C=VoltJ/C=Volt

...2

2

1

1 r

Qk

r

QkVp

Potential DifferencePotential Difference

ABAB VVV

Work done to move an unit charge Work done to move an unit charge from A to Bfrom A to B

Work done to move charge QWork done to move charge Q

W can be either positive or negativeW can be either positive or negative

QVW

ExampleExample

Car battery (12V)Car battery (12V) Work done to move a proton from A Work done to move a proton from A

to Bto B Work done to move an electron from Work done to move an electron from

A to BA to B

Potential EnergyPotential Energy

Potential energy of charge Q: QVPotential energy of charge Q: QV When a charge moves through When a charge moves through

potential V, gain (loss) kinetic energypotential V, gain (loss) kinetic energy Proton accelerated by 3MV, find its Proton accelerated by 3MV, find its

speed.speed. Television TubeTelevision Tube More about protonMore about proton Charge particle with charge Charge particle with charge nene

ExamplesExamples

Two 6 C charges 10 cm apart, find V Two 6 C charges 10 cm apart, find V and E at various pointsand E at various points

Acceleration of a proton by electric Acceleration of a proton by electric field E=500 N/C.field E=500 N/C.

Coulomb force between two identical Coulomb force between two identical chargescharges