unit three no area of electricity and magnetism live …dristle/ppt_ch_12.pdfunit three electricity...

UNIT THREEUNIT THREE

ElectricityElectricity

andand

MagnetismMagnetism

No area ofphysics has had

a greater impacton the way we

live than thestudy of

electricity andmagnetism.

Chapter 12Chapter 12

ElectrostaticElectrostatic

PhenomenaPhenomena

What doeslightninghave in

common...

... with hairon a dry

winter day?

Effects of Electric

Charge! Hair seems to have a mind of its own when

combed on a dry winter day.

! What causes the hairs to repel one another?

"Why does a piece of

plastic refuse to leave your

hand after you peeled it off

a package?

"Why do you get a slight

shock after walking across

carpet and touching a light

switch?

! All these phenomena involve different materials rubbingagainst one another.# Electrostatic effects can be demonstrated by rubbing plastic or glass

rods with different furs or fabrics.

# Small wads of dry, paperlike material called pith balls are lightenough to be strongly influenced by electrostatic forces.

# When a plastic rod, vigorously rubbed with cat fur, is brought nearthe pith balls, at first the pith balls are attracted to the rod like bits ofiron to a magnet.

# After contacting the rod, the pith ballsdance away from the rod.

# They are now repelled by the rod andalso by each other.

! A repulsive force must be acting between the two pith ballsafter they have been in contact with the rod.# Perhaps the balls have received something (call it electric charge)

from the rod that is responsible for the force we observe.

# This charge was somehow generated by rubbing the rod with the catfur.

# The force that is exerted by one stationary charge on another iscalled the electrostatic force.

! Experiments with different materials indicate that there aretwo types of charge.

! An electroscope consists of two metallic-foil leavessuspended from a metal post inside a glass-walledcontainer.# If the foil leaves are uncharged, they will hang straight down.

# If a charged rod is brought in contact with the metal ball on top, theleaves immediately spread apart and stay apart, even if the rod isremoved.

# If an object of the same charge as theoriginal rod is later brought near themetal ball, the leaves will spreadfarther apart.

# An object with the opposite charge willmake the leaves come closer together.

# A larger charge produces a largereffect.

Like charges repel each other,

and unlike charges attract

each other.

! Benjamin Franklin introduced the names positive andnegative for the two types of charge.

! He also proposed that a singlefluid was being transferredfrom one object to anotherduring charging.# A positive charge resulted from

a surplus of the fluid, and anegative charge resulted froma shortage of the fluid.

# Franklin arbitrarily proposedthat the charge on a glass rodwhen rubbed with silk be calledpositive.



each other.

! Franklin’s model comes surprisingly close to our modernview.

! When objects are rubbed together, electrons may betransferred from one objectto the other.# Electrons are small, negatively

charged particles present in allatoms and, therefore, in allmaterials.

# A negatively charged object hasa surplus of electrons, and apositively charged object has ashortage of electrons.

# The atomic or chemical propertiesof materials dictate which way theelectrons flow when objects arerubbed together.



each other.

Conductors and

Insulators! Different materials behave differently in the

presence of electrostatic forces.# Charge can readily flow through conductors:

# metals, like copper, silver, iron, gold; our bodies

# Materials that do not ordinarily permit charge toflow are insulators:

# plastic; glass; ceramics; other nonmetallic materials

# Charge flows much more readily through severalmiles of copper wire than through the few inchesof insulating ceramic material.

# Semiconductors are intermediate between agood conductor and a good insulator.

# Their importance to modern technology is enormous.

Can you charge an object withoutactually touching it with another

charged object?

! Charging by inductioninvolves the conductingproperty of metals:# Charge a plastic rod with

cat fur and bring the rodnear a metal ball mountedon an insulating post.

# The electrons in the metalball are repelled by thenegative rod.

# There is a negative chargebuildup on the side oppositethe rod, and a positivecharge on the near side.

Can you charge an object withoutactually touching it with another

charged object?

! To charge the ball byinduction, now touch theball with your finger on theside opposite the rod.# The negative charge flows

from the ball to your body,since it is still repelled bythe negative rod.

# If you now remove yourfinger and then the rod, anet positive charge is left onthe ball.

! Charging by induction illustrates the mobility ofcharges on a conducting object such as the metalball.# The process will not work with a glass ball.

# Charging by induction is an important process inmachines used for generating electrostatic charges, andin many other practical devices.

# It also explains some of the phenomena associated withlightning storms.

Why are insulators attracted tocharged objects?

! Recall that the pith ballswere attracted to thecharged rod before theywere charged themselves.# Electrons are not free to move

in the insulating material of thepith balls.

# However, within each atom ormolecule, charges can move.

# Each atom becomes anelectric dipole: the center ofthe negative charge is slightlydisplaced from the center ofthe positive charge.

# The material is polarized.

! Since the negatively charged surface is closer tothe rod than the positively charged surface, itexperiences a stronger electrostatic force.# The overall effect is that the pith ball is attracted to the

charged rod, even though the net (total) charge on thepith ball is zero.

# After the ball comes in contact with the charged rod,some of the charge on therod is transferred to thepith ball.

# The pith ball is thenpositively charged like therod, and so is repelled bythe rod.

! Polarization explains why small bits of paper orstyrofoam are attracted to a charged object suchas a sweater rubbed against some other material.

! Electrostatic precipitators used to remove particlesfrom smoke in industrial smoke stacks use thisproperty.# Polarized particles are attracted to charged plates in the

precipitator, removing them from the emitted gases.

The Electrostatic Force:

Coulomb’s Law! Coulomb measured how the

electrostatic force varies withdistance and quantity ofcharge.# Since the electrostatic force is

so weak, he had to developspecial techniques, involving atorsion balance.

# The degree of twist of the wiremeasures the repulsive forcebetween the two charges.

! Determining the amount ofcharge on the balls wasmore difficult.

! Although he could not measure absolute quantitiesof charge on the balls, Coulomb was able tomeasure the effects due to different relativeamounts of charge.# By bringing two identical metal balls into contact, one

charged and the other initially uncharged, Coulomb knewhe had equal amounts of charge on both balls.

# By repeating the process, he could get a ball with exactlyhalf that charge, or one-fourth, etc.

# He could then measurehow the strength of theelectrostatic force variedwhen the amount ofcharge was doubled,quadrupled, etc., inaddition to how the forcevaried with distancebetween the balls.

Coulomb’s Law

! The electrostatic force between two chargedobjects is proportional to the quantity of eachof the charges and inversely proportional tothe square of each distance between thecharges.

!

F =kq1q2

r2

in units of coulombs (C)

Coulomb's constant k = 9 "109 N #m

2/C

2

Two positive charges, one 2 µC and theother 7 µC, are separated by a distanceof 20 cm. What is the magnitude of the

electrostatic force that each chargeexerts upon the other?

a) 0.32 Nb) 0.63 Nc) 0.70 Nd) 2.02 Ne) 3.15 N

!

q1

= 2 µC q2

= 7 µC r = 20 cm = 0.2 m

F =kq

1q

2

r2

=9 "10

9 N #m

2/C

2( ) 2 "10$6

C( ) 7 "10$6

C( )0.2 m( )

2

=0.126 N #m

2

0.04 m2

= 3.15 N

! The electrostatic force has the same inverse-squaredependence on distance as Newton’s law ofgravitation.

# If we double the distance between the charges, the forcefalls to one-fourth of the original.

# The gravitational force depends on the masses, and theelectrostatic force depends on the charges.

# Gravity is always attractive; there is no such thing asnegative mass.

# Gravity is much weaker than the electrostatic force.

# Physicists are still trying to understand the reasons for therelative strengths of the fundamental forces.

# The search for a unified field theory that would explain therelationships between all of the fundamental forces is amajor area of research in modern theoretical physics.

!

Fg =Gm

1m

2

r2

and Fe =kq

1q

2

r2

Three positive charges are located along a line asshown. What is the magnitude of the force exerted

on the 0.02-C charge by the 0.10-C charge?

a) 2.25 x 106 Nb) 4.5 x 106 Nc) 9.0 x 106 Nd) 1.8 x 107 Ne) 2.7 x 108 N

!

q1 = 0.02 C q2 = 0.10 C r = 2 m

F =kq1q2

r2

=9 "109 N #m2 /C2( ) 0.02 C( ) 0.10 C( )

2 m( )2

= 4.5 "106 N (to the right)

Three positive charges are located along a line asshown. What is the magnitude of the force exerted

on the 0.02-C charge by the 0.04-C charge?


!

q1 = 0.02 C q2 = 0.04 C r = 1 m

F =kq1q2

r2

=9 "10

9 N #m

2/C

2( ) 0.02 C( ) 0.04 C( )

1 m( )2

= 7.2 "106 N (to the left)

Three positive charges are located along a line asshown. What is the net force exerted on the 0.02-C

charge by the other two charges?


!

F = F1 " F2

= 7.2 #106 N " 4.5 #10

6 N

= 2.7 #106 N (to the left)

The Electric Field

! How do the charges exert forces on eachother, when they are not even touching?# The concept of an electric field describes how

one charge affects the space around it, which thenexerts a force on another charge.

# The electric field at a given point in space is theelectric force per unit positive charge that wouldbe exerted on a charge if it were placed at thatpoint.

# It is a vector having the same direction as theforce on a positive charge placed at that point.

!

E =F

q

Two point charges, 3 µC and 2 µC, are separatedby a distance of 30 cm. A third charge q0 isplaced between them as shown. The forceexerted by q1 on q0 is 10.8 N, and the force

exerted by q2 on q0 is 1.8 N.What is the net electrostatic force acting on q0?

a) 1.8 N to the leftb) 9 N to the rightc) 10.8 N to the rightd) 12.6 N to the righte) 12.6 N to the left

!

F = F1 " F2

= 10.8 N "1.8 N

= 9 N (to the right)

What is the electric field at the location of thecharge q0 due to the other two charges?

a) 2.25 N/C to the leftb) 3.0 N/C to the leftc) 4.5 N/C to the leftd) 2.25 N/C to the righte) 3.0 N/C to the rightf) 4.5 N/C to the right

!

E =F

q0

=9 N

4 "10-6 C

= 2.25 "106 N/C (to the right)

! We can then use the field to find the force onany other charge placed at that point:

# If the charge q is negative, the minus sign indicates that thedirection of the force on a negative charge is opposite to thedirection of the field.

# The direction of the electric field is the direction of the forceexerted on a positive test charge.

# We can talk about the field at a point in space even if there isno charge at that point.

# The electric field can exist even in a vacuum.

# The field concept can also be used to define a gravitationalfield or a magnetic field, as well as others.

!Although Maxwell was the majorcontributor to the electric field concept,Faraday also developed the idea of fieldlines as a means of visualizing both thedirection and strength of the field.

$The direction of the electricfield lines around a positivecharge can be found byimagining a positive testcharge q0 placed at variouspoints around the sourcecharge.

$The field has the samedirection as the force on apositive test charge.


$The electric field linesassociated with a positivecharge are directed radiallyoutward.


$A positive test charge isattracted to a negativecharge.

$The electric field linesassociated with a negativecharge are directed inward,as indicated by the force ona positive test charge, q0.

!An electric dipole is two charges of equalmagnitude but opposite sign, separatedby a small distance.# Electric field lines originate on positive

charges and end on negative charges.

$The field lines point awayfrom the positive charge, andin toward the negativecharge.

$Near each charge, theelectric field approximatesthe field due to a single pointcharge of the same sign.

Two charges, of equal magnitude but opposite sign, liealong a line as shown. What are the directions of the

electric field at points A, B, C, and D?a) A:left, B:left, C:right, D:rightb) A:left, B:right, C:right, D:rightc) A:left, B:right, C:right, D:leftd) A:right, B:left, C:left, D:righte) A:right, B:left, C:right, D:right

Electric Potential

! The electrostatic force is a conservative force,which means we can define an electrostaticpotential energy.# We can therefore define electric potential or

voltage.

$Two parallel metal platescontaining equal butopposite charges producea uniform electric fieldbetween the plates.

$This arrangement is anexample of a capacitor, adevice to store charge.

! A positive test charge placed in the uniform electricfield will experience an electrostatic force in thedirection of the electric field.

! An external force F, equal in magnitude to theelectrostatic force qE, will move the charge q adistance d in the uniform field.

$The external force does workon the charge and increases thepotential energy of the charge.

$The work done by the externalforce is qEd, the force times thedistance.

$This is equal to the increase inpotential energy of the charge:!PE = qEd.

$This is analogous to whathappens when a mass m is liftedagainst the gravitational force.

! Electric potential is related to electrostatic potentialenergy in much the same way as electric field is relatedto electrostatic force.

! The change in electric potential is equal to the changein electrostatic potential energy per unit of positive testcharge:

! Electric potential and potential energy are closelyrelated, but they are NOT the same.# If the charge q is negative, its potential energy will decrease

when it is moved in the direction of increasing electricpotential.

! It is the change in potential energy that is meaningful.

!

"V ="PE

q in units of volts (V)

1 J/C = 1 V

"PE = q"V

Two plates are oppositely charged so that they have auniform electric field of 1000 N/C between them, asshown. A particle with a charge of +0.005 C is moved

from the bottom (negative) plate to the top plate.What is the change in potential energy of the

charge?a) 0.15 Jb) 0.3 Jc) 0.5 Jd) 0.8 Je) 1.5 J

!

"PE =W = Fd = qEd

= (0.005 C)(1000 N/C)(0.03m)

= 0.15 J

What is the change in electric potential from thebottom to the top plate?

a) 0.15 Vb) 0.3 Vc) 5 Vd) 30 Ve) 150 V

!

"V ="PE

q=

0.15 J

0.005 C= 30 V

! The potential energy of a positive chargeincreases when we move it against the field.

# For a uniform electric field, there is a simplerelationship between the magnitude of the electricfield and the change in electric potential: !V = Ed.

$For non-uniform fields, therelationship is morecomplicated, but the electricpotential always increasesmost rapidly in the directionopposite to the electric field.

$For a positive point charge,the electric potentialincreases as we move closerto the charge.

What is lightning?What is lightning?

! Most thunderclouds generate a separation ofcharge resulting in a net positive charge near thetop and a net negative charge near the bottom.

! The charge separation produces strong electricfields in the cloud as well as between the cloud andearth.

! Since moist earth is a reasonably good conductor, apositive charge is induced on the surface of theearth below the cloud.

!! Most thunderclouds generate a separation ofMost thunderclouds generate a separation ofcharge resulting in a net positive charge near thecharge resulting in a net positive charge near thetop and a net negative charge near the bottom.top and a net negative charge near the bottom.

!! The charge separation produces strong electricThe charge separation produces strong electricfields in the cloud as well as between the cloud andfields in the cloud as well as between the cloud andearth.earth.

!! Since moist earth is a reasonably good conductor, aSince moist earth is a reasonably good conductor, apositive charge is induced on the surface of thepositive charge is induced on the surface of theearth below the cloud.earth below the cloud.

! The electric field generated can be several thousand voltsper meter; the potential difference between the cloud’sbase and the earth can easily be several million volts!

! This creates an initial flow of charge (the “leader”) along apath that offers the best conducting properties over theshortest distance.

$The leader ionizes some of theatoms in the air along that path.

$The following strokes all takeplace along this same path inrapid succession.

$The heating and ionizingproduce the lightning we see.

$The thunder (sound waves) isproduced at the same time, buttakes longer to reach us sincesound travels slower than light.

unit three no area of electricity and magnetism live …dristle/ppt_ch_12.pdfunit three electricity...

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