ap ch 16-teacher

8/6/2019 AP Ch 16-Teacher

1/63

AP Physics Chapter 16

Electric Potential, Energy, andCapacitance


2/63

Chapter 16: Electric Potential, Energy,

and Capacitance16.1 Electric Potential and Potential

Difference

16.2 Equipotential Surfaces and theElectric Field

16.3 Capacitance

16.4 Omitted16.5 Capacitors in Series and in Parallel


3/63

Homework for Chapter 16

Read Chapter 16

HW 16.A: p.537-539: 4,8-13, 16,17, 20-23, 47,48, 51-53, 55-57.

HW 16.B: p.540-541: 64-70, 84-87, 89, 90.


4/63

B L A C K H O L E S A R E WH ERE GO

D D I V I D E D B Y ZE R O


5/63

If your car is traveling at the speed of light and

you turn your headlights on, what happens?

-StevenWright


6/63

16.1: Electric Potential andPotential Difference


7/63

Electric Potential Energy Difference

a) Movinga positive charge qo againsttheelectric fieldrequires positive workand

increasestheelectric potentialenergy.

Theforce requiredto movethe chargeisequaltotheelectric force:Fe = qo E

Thework done bythe force: Fe d= qo E d Theincreaseinthe chargeselectric potentialenergyisequaltothe workdone

onthe charge:Ue = UB UA = qo E d

The SI unitofelectric potentialenergyisthe joule (J).

b) Movinga mass m againstthegravitational fieldrequires positive workand

increasesthegravitational potentialenergy: Ug = UB UA = mgh


8/63

Electric Potential Difference

** This is not the same as Electric Potential Energy Difference**

Theelectric potential difference (voltage) betweentwo pointsisthe work per

unit positive chargedone byanexternal forcein moving charge betweenthese

two points,

OR

the changeinelectric potentialenergy perunit positive charge.

V = W = Ue where qo isthe positivetest charge

qo qo

The SI Unitofelectric potentialdifferenceis: joule/coulomb (J/C)orvolt (V).

Electric potentialdifferenceis commonlyshorted fromV to just V.

Potentialdifferenceisdefined perunit charge,soitdoesnotdependonthe

amountof charge moved (potentialenergydifferencedoes).


9/63

On Gold Sheet


10/63

Potential Difference for a Uniform Field Between Two Parallel Plates

Assume we wouldliketo movea positivetest charge, qo,from thenegativeto

the positive plate. This move would beagainsttheelectric field, wouldrequirework,and wouldincreasethe charges potentialenergy. The potentialdifference

betweenthe platesis:

V = W = Ue where qo isthe positivetest chargeand

qo qo Ueisthe potentialenergygained

Ina uniform electric fieldE,the potentialdifferencein movingthe chargethrough

astraightlinedistanced is:

V = Ue = qoE d = E d Potential Difference

qo qo Parallel Plates

Whentalkingaboutelectric potential, wealways mustdefinethereference

value. Only changesinelectric potential (voltage)are meaningful.

ex: Thenegative plateis commonlyassignedavalueof zero,sovoltage

will be positive.


11/63

Positive charges, when released, tend to move toward regions of low potential,

and negative charges tend to move toward regions of high potential.

Acceleratinga Charge

a) Movinga proton from thenegativetothe positive plateincreasesthe

protons potentialenergy.

b) Whenitisreleased from the positive plate,the protonaccelerates back

towardthenegative plate,gainingkinetic energyandlosingelectric potentialenergy.

c) The workdoneto movea proton betweenanytwo pointsintheelectric field

is INDEPENDENT OF PATH.


12/63

Example 16.1: Anelectroninitiallyatrest,isacceleratedthrough anelectric

potentialdifferenceof 50.0 V.

a) Whatisthekinetic energyoftheelectron?

b) Whatisthespeedoftheelectron?


13/63

Example 16.2:A 12-V battery maintainstheelectric potentialdifference between

tow parallel metal platesseparated by 0.10 m. Whatistheelectric field between

the plates?


14/63

A positive point charge createsanelectric field.

Theelectric potential

increasesasyou move closer

tothe positive charge.

SincerB < rA, B isata higher

potentialthan A,andthe

potentialdifferenceis positive.

Electric potential increases (+V) as we get closer to positive charges or fartheraway from negative charges.

Electric potential decreases (-V) as we get farther away from positive charges

or nearer to negative charges.

Potential Difference Due to Point Charges


15/63

On Gold Sheet


16/63

Electric Potential

V =kq electric potentialduetoa point charge

r ( V = 0 atr=g)

Unlikeelectric field,electric potentialisascalarquantity. Whenadding

potentialsdueto point charges, justaddthem algebraically (includingthe + or

signs).

V =k i qi

ri

Note:onthegoldsheet, Coulombslaw constantis writtenas 1/4TIo.

Anotherdifference betweenelectric fieldandelectric potentialisnotable:

electric fieldis proportionalto 1/r2

electric potentialis proportionalto 1/r

On Gold Sheet


17/63

On Gold Sheet


18/63

Electric Potential Energy of Various Charge Configurations

a) A positive point charge q1 is fixedinspaceandasecond positive charge q2 is

pushedtowardit from averylargedistance (r=g

)toadistancer12.

Thereisanincreasein potentialenergy because positive work must bedone

to bringthe mutuallyrepelling charges closertogether.


19/63

Electric Potential Energy of Various Charge Configurations

Formorethantwo charges,thesystemselectric potentialenergyisthesum ofthe

energiesofeach pair.

Electric Potential Energy followsthe Law

of Conservationof Energy. Forexample,

considertwo protonsthatare heldneareach otheratrest. Work wasdoneto

bringthem close,andstoredinthe form

ofelectric potentialenergy. If werelease

them,they will flyapart. Theelectric

potentialenergy will be convertedto

kinetic energy. Thisisverysimilartotwomasses connected bya compressed

spring.


20/63

Example 16.3: A chargeof 5.0 nC isat (0,0)andasecond chargeof -2.0 nC isat

(3.0m, 0m). Ifthe potentialistakento be zeroatinfinity,

a) whatistheelectric potentialat point P (0,4.0) m?b) whatisthe potentialenergyofa 1.0 nC chargeat point P?

c) whatisthe workrequiredto bringa chargeof 1.0 nC charge from infinityto

point P?

d) whatisthetotal potentialenergyofthethree chargesystem?


21/63


22/63

Summary:

Theelectric potentialdifference betweentwo pointsisthe work perunit positive

chargedone byanexternal forcein moving charge betweenthosetwo points.

Electric potentialdifferenceisthe changeinelectric potentialenergy perunit

positive charge.

Voltageissynonymous with electric potentialdifference.

V = W = Ue electric potentialdifference (voltage)definitionqo qo

V = Ed electric potentialdifference between parallel plates

V =kq electric potentialduetoa point charge (V = 0 atr=g)r

U = U12 + U23 + U13 + electric potentialenergyofa configurationof point

charges


23/63

2. Whatisthedifference betweenelectrostatic potentialenergyandelectrostatic

potential?

Answer: Potentialisthe potentialenergy perunit charge: V = Ue / qo

3. Whatisthedifference betweenelectric potentialdifferenceandvoltage?

Answer:nodifference.

Check forUnderstanding:

1.The SI unitofelectric potentialdifferenceisthe

a) jouleb)newton

c)newton-meter

d) joule percoulomb

Answer:d


24/63

Check forUnderstanding:

4. Theelectrostatic potentialenergyoftwo point charges

a)isinversely proportionaltotheirseparationdistance

b)isavectorquantity

c)isalways positive

d) has unitsofnewton percoulomb

Answer: a,since potentialenergyisinversely proportionaltothedistance betweenthe charges.

5. Anelectronisreleasedinaregion wherethereisavaryingelectric

potential. Theelectron will

a) movetowardthelowerpotentialregion

b) movetowardthe higherpotentialregion

c)remainatrest

Answer: b, becausetheelectron hasanegative charge


25/63


26/63


27/63

I lived in a house that ran on static electricity...

If you wanted to run the blender, you had to

rub balloons on your head. If you wanted to

cook, you had to pull off a sweater real quick.

-StevenWright


28/63

16.2: Equipotential Surfaces andthe Electric Field


29/63

Construction of Equipotential Surfaces Between Parallel Plates

Considera positive charge moving from A to A

perpendiculartoanelectric field.

Sincetheelectric fieldis perpendiculartothe

displacement,no workisdone bythe field.

Ifno work wasdone,thentheelectric potential

energyofthe charge mustnot have changed.

We can concludeall pointson path I havethe

sameelectric potentialenergy,andthereforethe

same potential.

We canextendthistoall pointsonthe planeparalleltothe plates containing path I.

Such a plane,is calledanequipotential surface,

orsimply anequipotential.

Since path II startsandstopsonthesameequipotential,no work wasdone.


30/63

Equipotential Surfaces Between Parallel Plates

Onceyou movetoa higherpotential (A to B),you can

stayonthatnew equipotential by movingperpendicularlytotheelectric field. (B to B).

The changein potentialisindependentof path,since

thesame changeoccursvia path I asvia path II.

Since no work is required to move a charge along an equipotential surface,then it must be generally true that equipotential surfaces are always at rightangles to the electric field.


31/63

Gravitational Potential Energy as an Analogy

Raisinganobjectaway from theearth resultsinanincreaseintheobjects

potentialenergy.

Atagiven height,its potentialenergyis constantaslongasitremainsonthat

equipotentialsurface.


32/63

Topographic Maps: A Gravitational Analogy for Equipotential Surfaces

Considerasymmetrical hill with slicesatdifferentelevations. Each sliceisa planeof constantgravitational potential.

Hereisanoverheadview,ortopographic

map,ofthe hill.

The contours, wherethe planesintersectthe

surface,representgravitationalequipotentials.


33/63

Topographic Maps: A Gravitational Analogy for Equipotential Surfaces

The potential V arounda

point charge formsasymmetrical hill.

V is constantat fixed

distances from q.

Electricalequipotentialsarounda point chargearespherical,orintwodimensions, circular

slices.


34/63

Equipotentials of an Electric Dipole

Equipotentialsare perpendicularto

electric fieldlines.

Noticethat V1 > V2,sinceequipotential

surface 1 is closertothe positive charge

thanissurface 2.

Activity: Learn by Drawing, p. 522.

Animation:

http://regentsprep.org/Regents/physics/phy

s03/aequilines/default.htm


35/63

Electric Field From Potential

Ina uniform electric field,such asone

betweentwo parallel plates,the potential

difference betweenanytwoequipotentialplanes,separated byadistance xis

V = E x

Foragiventraveldistance x, movement

perpendiculartotheequipotentialsvieldsmaximum potentialgain.

By findingthedirectionof maximum

potential change, weare findingthedirection

oppositethatofthe E field.

E = - V electric field

x max from potentialOn Gold Sheet


36/63

Electric Field from Potential

E = - V electric fieldx max from potential

The minussignindicatesthat E isinthedirectionoppositethatin which V

increases mostrapidly,orinthedirection V decreases mostrapidly.

The unitsofelectric fieldarevolts permeter(V/m). Thisisdimensionallyequivalentto N/C, which welearnedaboutin Chapter15. (Proveit!)

Answer: V = J/C = J = Nm = N

m m Cm Cm C


37/63

Example 16.4: Two parallel plates,separated by 0.10 m,are connectedtoa 6.0 V

battery. Anelectronisreleased from restatthenegative plate.


38/63

The Electron Volt

electronvolt (eV) - thekinetic energyacquired byanelectron

acceleratedthrough a potentialdifferenceofexactly 1 V.

1 eV = 1.60 x 10-19 J

Theelectronvoltisa convenient waytoexpresstypicalenergiesontheatomic

scale.

Theelectronvoltisa unitofenergy,notvoltage: e V = q V = Ue

You mayalsoencounter keV: kiloelectron volts, meaning1000 eV

MeV: megaelectron volts, meaning106 eV

GeV: gigaelectron volts, meaning109

eV

** Warning electronvoltisnotan SI unit. You must convert backto joules before

you can usethenumberina formula**


39/63

Summary

Equipotential surfaces (equipotentials)aresurfaceson which a charge hasa

constantelectric potential (V),and constantelectric potentialenergy (Ue).

Equipotentials are perpendiculartotheelectric fieldatall points.

Ittakesno workto movea chargealonganequipotential.

E isinthedirectionoppositethatin which V increases mostrapidly,orinthe

directionin which V decreases mostrapidly.

Anelectronvolt (eV)isthekinetic energygained byanelectronaccelerated

from restthrough a potentialdifferenceof 1 V.

1 eV = 1.60 x 10-19 J

E = - V relationship between potentialandelectric field

x max


40/63

Check forUnderstanding

1) Equipotential surfacesarethosesurfaceson which

a) the potentialis constant

b) theelectric fieldis zero

c) the potentialis zero

Answer:a

2) Equipotential Surfacesare

a) paralleltotheelectric field

b) perpendiculartotheelectric field

c)atanyangle with respecttotheelectric field

Answer: b


41/63


3) Between charged parallel plates, which equipotentials havea higherpotential:

a)theonesnearthe positive plate

b)theonesnearthenegative plate

c)theonesnearthe middle?

Answer:a

4) Atagiven pointonanequipotentialsurface,theelectric field pointsdirectly

tothe

a)next highestequipotential

b)thenextlowestequipotential

c) paralleltotheequipotentialsurface

Answer: b

HW 16.A: p.537-539:4,8-13, 16,17, 20-23,47,48, 51-53, 55-57.


42/63

I heard that in relativity theory space and time

are the same thing.

Einstein discovered this when he kept showing

up three miles late for his meetings.

-StevenWright


43/63

16.3: Capacitance


44/63

Capacitance

A capacitorconsistsoftwo conductors.

Capacitorsstore charge,andthereforeelectric energy,inthe form ofanelectric field.

capacitance (C) - a quantitative measureof how effectivea capacitor

isinstoring charge.

C = Q definitionof capacitance

V

where Q isthe magnitudeofthe chargeoneitherplate (the plates haveequal butopposite charge),and V isthe potentialdifferenceacrossthe plates

Note, from this pointon we will use V forV; it means potentialdifference.

assorted capacitors


45/63

Metal plates

+Q

Capacitor and Circuit Diagram

Two metal platesare charged bya batterytoa charge Q = CV, where C isthe

capacitance.

Workisdonein chargingthe capacitor,andenergyisstoredintheelectric field.

Noticethesymbols used fora battery (V)anda capacitor(C).

parallel linesare equal inlength

the longer line of the batterysymbol is the positive terminal


46/63

Capacitance

The battery worksasa pump toremoveelectrons from the positive plateand

transferthem through the wiretothenegative plate.

The battery chargesthe capacitoruntilthe potentialdifference betweenthe

platesisequaltothevoltageofthe battery.

Whenthe batteryisdisconnected from the capacitor,theelectric potential

energyisstoredintheelectric field. Thisstoredenergy canthen be usedtodo

work.

The SI unitof capacitanceis coulomb pervolt (C/V),or farad (F).

Itis more commontoseethe microfarad ( 1 QF = 10-6 F)

orthe picofarad (1 pF = 10-12 F)

The farad wasnamed forthe English scientistMichael Faraday (1791-1867),anearlyinvestigatorofelectrical phenomena who firstintroducedthe conceptofthe

electric field.


47/63

Capacitance

Capacitancedependsonlyonthesize,shapeandspacingofthe plate

arrangement,as wellatthe material betweenthe plates (dielectric).

A common capacitoristhe parallel plate capacitor. It consistsoftwo metal plates

ofarea A andseparated byadistanced. The formulais:

C =IoA capacitanceofa parallel-plate

d capacitor(inair) Ioisthepermittivityof freespace.Itisa fundamental constant which describes

theelectrical propertiesofavacuum. Itsvalueinairisessentiallythesame.

Io =8.85 x 10-12 C2/(Nm2)

IoisrelatedtoCoulombs constantby:

k= 1 = 9.00 x 109 Nm2/C2

4TIo

On Blue Sheet

On Blue Sheet

On Gold Sheet


48/63

Capacitance

A plotof chargevs.voltage fora charging capacitorisastraightline with slope C.

Q = CV( y= mx + b)

The workdone bythe batteryisstoredinthe capacitoras potentialenergy, Uc.

This workisthearea underthe curve. Therefore, Uc = Q V.

Theequivalent formsofthisequationare:

Uc = QV = Q2 = CV2 energystorage2C ina capacitor

The form CV2 is usuallythe most practical,sincethe capacitanceandthe

appliedvoltageareoftenknownorcan be measured mosteasily.

Voltage

Q

(charge)

slope=

CapacitanceOn Gold Sheet

On Gold Sheet


49/63

Example 16.5:A parallel-plate capacitorconsistsof platesofarea 1.5 x 10-4 m2

andseparated by 2.0 mm. The capacitoris connectedtoa 12 volt battery.

a) Whatisthe capacitance?b) Whatisthe chargeonthe plates?

c) How much energyisstoredinthe capacitor?

d) Whatistheelectric field betweenthe plates?


50/63

If youre not part of the solution, youre part

of the precipitate.

-StevenWright


51/63

16.5: Capacitors in Series and inParallel

Capacitors can be connectedintwo basic ways:inseriesorin parallel.

Inseries capacitorsare connected headtotail.

In parallel capacitors havealltheirheads hookedtogether,andall

theirtails hookedtogether.


52/63

Capacitors in Series

All capacitorsinseries havethesame charge.

Thesum ofthevoltagedropsisequaltothevoltageofthe battery.

Thetotal capacitanceisequivalentto Cs,ortheequivalentseries capacitance.

Cs isalwayslessthanthatofthesmallest capacitorinthe combination.


53/63

Capacitors in Series

When capacitorsare wiredinseriesthe chargeisthesameonallthe plates.

Q = Q1 = Q2 = Q3 =

Thevoltagedrop acrossallthe capacitors must beequaltothevoltageacrossthebattery.

Therefore,thesum oftheindividualvoltagedropsacrossthe capacitorsisequalto

thevoltageofthe battery. V =V1 + V2 + V3 +

Theindividualvoltagesarerelatedtotheindividual charges byV1 =Q, V2 =Q, V3 =Q, andV =Q

C1 C2 C3 Cs

Substituting Q/C forV: Q = Q + Q + Q +

Cs C1 C2 C3

Dividing both sidesoftheequation by Q: 1 = 1 + 1 + 1 +...

equivalent series capacitance Cs C1 C2 C3


54/63

Capacitors in Parallel

Whenthe capacitorsarein parallel,thevoltagesacrossthe capacitorsare

thesame.

Thetotal chargeisequaltothesum ofthe chargesontheindividual

capacitors.

Thetotal capacitanceisequivalentto Cp.

Cp isalwayslargerthanthatofthelargest capacitorinthe combination.


55/63

Capacitors in Parallel

When capacitorsare wiredin parallelthevoltagesacrossthe capacitorsarethe

same,each equaltothevoltageofthe battery

V = V1 = V2 = V3 =

Thetotalstored chargeisequaltothesum ofthe chargesoftheindividual

capacitors.

Qtotal = Q1 + Q2 + Q3 +

Theindividual chargesaregiven by Q1 = C1V, Q2 = C2V, and Qtotal = CpV

Substituting CV forQ: CpV = C1V + C2V + C3V +

Divide both sidesoftheequation by V:

equivalent parallel capacitance Cp = C1 + C2 + C3 +


56/63

On Gold Sheet


57/63

Example 16.7: Capacitors C1 and C2 arein parallel. This combinationisinseries

with C3. The positiveterminalofa 12.0 V batteryis connectedto C3.

C1 = 6.00 QF, C2 =8.00 QF, C3 = 14.0 QF

a) Whatistheequivalent capacitance?b) Whatisthe chargeofeach capacitor?

c) Whatisthevoltageacrosseach capacitor?


58/63


59/63

Summary

A capacitorstores charge,andthereforeelectric energy,inthe form ofanelectric

field.

Capacitanceisa quantitative measureof how effectivea capacitorisinstoring

charge.

Theequivalentseries capacitanceisalwayslessthanthatofthesmallest

capacitoroftheseries combination.

Theequivalent parallel capacitanceisalwayslargerthanthatofthelargest

capacitorinthe parallel combination.


60/63

Summaryof Equations

C = Q definitionof capacitance

V

C =IoA capacitanceofa parallel-plate

d capacitor(inair)

Uc = QV = Q2 = CV2 energyina2C charged capacitor

1 = 1 + 1 + 1 +... equivalent series capacitance

Cs C1 C2 C3

Cp = C1 + C2 + C3 + equivalent parallel capacitance


61/63


1. Capacitance has unitsof

a. farads

b. joules

c. coulombs pervolt

d. both a.and c.

Answer:d.

2. Toincreasethe capacitanceandtheenergy-storage capabilityofa parallel-plate

capacitor, we can

a.increasethe plateseparationdistance

b.increasethe platearea

c.evacuatethespace betweenthe plates

d.noneoftheabove

Answer: b,asthe capacitanceisdirectly proportionaltothe platearea,

C =IoA

d


62/63


3. Capacitorsinseries havethesame

a. voltage

b. charge

c. energystorage

Answer: b

4. Capacitorsin parallel havethesamea.voltage

b. charge

c.energystorage

Answer:a


63/63


5. Underwhat conditions wouldtwo capacitorsinseries havethesamevoltage?

Answer: Whentheyareequalin capacitance.

HW 16.B: p.540-541: 64-70,84-87,89,90.

ap ch 16-teacher

Documents