Unit 4 Physics Onthemove2_print2011_2

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Physics (9PH01) LECTURE NOTES

PHYSICS 9PH01)

LECTURE NOTES

Unit 4: Physics on the Move 6PH04/01)

TOPIC 2 Electric and Magnetic field

2.1 Electric Fields

2.2 Capacitors

2.3 Electromagnetic Effects



Physics (9PH01) Unit 4: Physics on the Move

- 2 -

Unit 4: TOPIC 2 Electric and Magnetic Field

2.1 Electric Fields2.1.1 Pushing Charges

1. Anelectricfieldcanbeusedtoaccelerateachargeparticle.

2. InX-raymachine,X-rayisproducedwhenthetungstentarget(anode)isbombardedbyelectronsathighspeed.

3. Averyhighelectricfieldisappliedonelectronsinordertoacceleratetheelectronstomoveathighspeed.

Figure 2.1 X-ray [source a)]

Electrical FieldDefinition

4. Regionwherethereareelectricalforcesactingoncharges

Electrical Field StrengthDefinition

5. Electrical field strength, E atapointinanelectricfieldisdefinedaselectricalforceofattractionexertedbytheelectricfieldperunitcharge.

= E - 2.1)

where − F Electrostaticforce

−q Charge




- 3 -

AccordingtoNewton’sSecondLawofmotion,

ma F =

Electrostaticforce,

qE F =

Hence,theaccelerationoftheelectron,

=a - 2.2)

where − E Electricalfieldstrength−q Chargeofelectron

2.1.2 Uniform and radial fieldsUniform Electric Field

6. Theelectricalfieldstrengthinequalatallthepointthelinesbetweentwoplatesareparallelandequallyspaced.

Figure 2.2 Uniform electric field [Source: e)]

Electric potential difference.

Electrical Potential

7. Electrical potential,V atapointinanelectricfieldisdefinedaselectricalpotentialenergyperunitcharge.

=V - 2.3)where −W Electrostaticenergy




- 4 -

8. Aswehavelearninunit2,workdonetobringcharge,Q fromonepointtoanother

pointwherethepotentialbetweentwopoint,V :

QV W =

9. Electrical potential for radial electric field,

=V - 2.4)

where −r distance

Page 41, question

Answer：

Page 41, question

Answer

：

Page 41, question

Answer：




- 5 -

Equipotential

10. Linejoiningpointsofequalpotentialenergyperunitcharge.

Figure 2.3 Equipotential curves and electric field lines for a) a constant E field, b) a

point charge, and c) an electric dipole. [source e)]

Potential Gradient

11. Rateatwhichpotentialdifferencechangeswithdistance.12. Asthedistance(frompositiveplate)increases,thepotentialdecreasesuniformly.

Figure 2.4 Potential-distance graph

13. Workdonetomoveacharge,Q underpotentialdifferenceofV isequaltothe

electricalforce, F appliedonthechargetomovetoadistanceof x .

gradient xV

Q F

QV Fx

==⇒

=

14. Thepotentialgradientisequaltotheelectricalfieldstrength.

UnitofQ

F E = is 1−NC andunitsof

x

V is 1−Vm .Theyarethesame.

0

Potential,V

Distance, x




- 6 -

Page 41, question

Answer：




- 7 -

Practice Questions

Solutions

Page 43, question

Answer：




- 8 -

Page 43, question

Answer：

2.1.3 Coulomb’s Law15. Considerasystemoftwopointcharges, 1Q and 2Q ,separatedbyadistance r in

vacuum.Theforceexertedby 2Q on 1Q isgivenbyCoulomb'slaw:

Theforcebetweentwochargesisdirectlyproportionaltotheproductoftheirchargeandinverselyproportionaltothesquareofthedistancebetweenthem.

2

21

r

QQ F α

- 2.6)

where − F Electrostaticforce

−21,QQ Charges

−r distancebetween_____________−k constant




- 9 -

22

4

1 −== CmN

o

k

πε

where −oε ________________________, 1121085.8 −−

× mF .

= F - 2.7)

Page 46, question

Answer：




- 10 -

2.2 Capacitors

2.2.1 Storing Charge

16. Acapacitorcanbechargedbyconnectingabatteryacrossit.

Figure 2.5 Charging a Capacitor [source b)]

17. ElectronsarerepelledbythenegativeterminalofthebatterytoplateYandelectrons

onplateXareattractedtothepositiveterminalofthebattery.

18. Duringthechargingprocess,therewillbeamomentarycurrentastheelectronsflow.

Thereadingwillreturntozerowhenvoltagebetweenthecapacitorthebatteryisthesame.

Capacitance Definition

19. Capacitor

20. Acapacitorisconsistedoftwoconductiveplatesseparatedbyaninsulatorcalledas

dielectric.

21. Symbol of a capacitor

Figure 2.6 Symbol of a) unpolarized capacitor b) polarized capacitor




- 11 -

22. Capacitance

=C - 2.8)

where −Q Charge

−V potentialdifference

Page 53, question

Answer：

Energy stored on a charged capacitor

23. Duringchargingprocess,thepotentialdifferencebetweentwoplatesincreasesaccordingtotheamountofchargestored.

C QV =

24. Hence,thepotentialdifferenceagainstchargestoredgraphasbelow:

Figure 2.9 Energy stored in a charged capacitor

25. Energystoredincapacitor, E =Areaundergraph

2

1= E - 2.11)

0

Potential

difference,

Charge, Q




- 12 -

OR

2

1= E

- 2.12)

Page 53, question

Answer：

2.2.2 Charging and discharging capacitorsGrowth and decay curves

Discharging capacitor maths

26. Whenaconductorisconnectedacrossachargedcapacitor,therewillbeflowofelectronsfromplateYtoplateX.Thecurrentwillstopwhenthevoltageacrossthetwoplatesiszero.

Figure 2.10 Discharging a Capacitor [source e)]

Exponential decay27. Charginganddischargingofcapacitorfollowtheexponentialdecay.




- 13 -

Charging of Capacitor28. Forcharging,thecurrentaftertime t ,

RC t

oe I I −

=

where −o I initialcurrent R

E I o =

− R resistance−C capacitance

29. Voltageaftertime t ,

)1( RC

t

e E V

−

−=

where − E electromotiveforce

30. Electric chargestoredincapacitoraftertime t

)1( RC

t

o eQQ−

−=

where CE Qo =

Graphs

Figure 2.11 Graph of charging a Capacitor

Discharging the Capacitor31. Fordischarging,thecurrentaftertime t ,

RC

t

oe I I −

= - 2.13)

where −o I initialcurrent

− R resistance−C capacitance

I

t0

V

t0

Q

t0




- 14 -

32. Voltageaftertime t ,

RC

t

EeV

−

= - 2.14)

where − E electromotiveforce

33. Electric chargestoredincapacitoraftertime t

RC

t

oeQQ−

= - 2.15)

where CE Qo =

Graphs

Figure 2.12 Graph of discharging a Capacitor

Time Constant,

34. Definition

Timetakenfor

=τ - 2.16)

where − R resistance

−C capacitance

Practice Questions

I

t0

V

t0

Q

t0




- 15 -

Solutions,

Page 53, question

Answer：

Page 53, question

Answer：

Page 59, question

Answer：




- 16 -

Page 59, question

Answer：

Page 59, question




- 17 -

Answer：




- 18 -

2.3 Electromagnetic Effects

2.3.1 Magnetic Fields

Pushing Poles

Permanent magnets.Magnetic field

35. Regionwheremagneticforcesareexperienced.

36. Likepolesrepelbutunlikepolesattract.

37. Themagneticfieldcanberepresentedbymagneticfieldlines.

38. Figure 2.13 showsthedirectionsmagneticfieldlinesareclearlyshownusingcompass.

Figure 2.13 Magnetic Field [source e)]

Fleming’s Left Hand Rules

Figure 2.14 Fleming’s Left-hand Rule [source f)]

39. Fleming’s Left-hand Rule helpsinidentifythedirectionofthemagneticforce(output)wherethedirectionofthemagneticfieldofpermanentmagnetandthedirectionof

3) THUMB – THRUST (Output), F

1) First Finger – Field, B (Point to South)

2) SeCond Finger – Electric Current, I




- 19 -

electriccurrentareidentifiedbeforehand.Figure 5.29 showsthemethodstoapplyFleming’sLeft-handRule.

40. Usingyourlefthand–firstfingershowsdirectionofmagneticfield,secondfinger

currentandthumbthethrust(offorce)ontheconductor.Page 63, question

Page 63, question

Answer




- 20 -

Practice Questions

Solutions ,




- 21 -

The Strength of Electromagnetic Force

Magnetic flux density (B-field).

Definition41. Forceperunitlengthperunitcurrentonacurrent-carryingconductoratrightanglestothefieldlines. - 2.17)

where − B magneticfieldstrength − F forceonthewireatrightangletofieldlines − I current −l lengthofwire

42. S.IunitofB istesla,T.

Notes:(a) BIl F =

(b) I B F ⊥⊥

43. Inmoregeneral,theforceproducedbycurrentandmagneticfieldonawire,

- 2.18)where −θ anglebetweenthecurrentandmagneticfield.

Figure 2.15 Force on a charged particle [source a)]




- 22 -

44. Theforce, F actingonachargedparticle, q inamagneticfieldwithstrength, B and

movingwithvelocity, v

- 2.19)

where − F forceonthechargedparticle− B magneticfieldstrength

−q chargeoftheparticle

−v velocityoftheparticle

Practice Questions

Solutions ,

Page 67, question

Answer




- 23 -

Page 67, question

Answer

Mass Spectrometer

45. Massspectrometeristheequipmentusedtoidentifyunknownchemicals.

Figure 2.16 Spectrometer [source a)]

46. Thechemicalischargedwhenenterthemachineandforceactsonthecharged

particleisamagneticfieldwhichisperpendiculartothedirectionmotionoftheparticle.




- 24 -

47. Thisforcealsomakestheparticlemovesincircularmotion.Therefore,

Bqv F = , ⇒= r

mv F

2

r

mv Bqv

2

=

Thecharge/massratio =m

q - 2.20)

48. Thekineticenergyoftheparticleisgainedbyapplyingpotentialdifference, V across

theparticle.

qV mv =2

2

1,

m

qV v

2=

=r - 2.21)

where −r radius−V potentialdifferenceapplied

−q chargeoftheparticle

−m massoftheparticle − B magneticfieldstrength

Ideas:

Page 67, question

[Given V=3000V,B=3T,e=1.6x10-19C,mp=mn=1.67x10-27kg]

Answer




- 25 -

2.3.2 Generating ElectricityElectromagnetic Induction

Phenomenon of Electromagnetic Induction

49. Wheneverthereisarelativemotionbetweenawireandamagnet,ane.m.f.willbeinducedinthewire. Flux linkage

Magnetic flux, flux linkage.Magnetic flux density

50. Ameasureofthestrengthofamagneticfield.

51. Tesla,T:unitofmagneticfluxdensity,where1Tproducesaforceof1N

52. Magneticfluxφ througharegionisameasureofthenumberofmagneticfieldlinethrougharegion.

- 2.22)

where − B magneticfluxdensity

− area

53. S.I.UnitofmagneticfluxisWeber(Wb).

Figure 2.17 Magnetic flux of single loop [source e)]

Page 71, question

Answer




- 26 -

Magnetic flux linkage54. Aproductofmagneticfieldandthenumberofturns.

55. Fluxlinkageisdefinedastheproductofthenumberofturns, N andthefluxthroughthecoil,

- 2.23)

Lenz’s Law

Definition

56. Thedirectionofaninducedemfissuchas

Figure 2.17 Lenz Law [source e)]

Calculating induced emfs

Faraday’s and Lenz’s laws of electromagnetic induction.Faraday’s Law

57. Magnitudeofinducede.m.finacircuitisdirectlyproportionaltotherateofchangeofmagneticfluxlinkagethroughthatcircuit.

- 2.24)

where −ε Inducedemf

−Φ∆ )( N Changeinfluxlinkage

−∆t Timetaken




- 27 -

Page 71, question

Answer

Page 71, question

Answer




- 28 -

Reference:

(a) EdexcelA2Physics,MilesHudson,Pearson(b) Fields,ForcesandSynthesis(Revisededition),MarkEllse&ChrisHoneywill.

Publisher:nelsonthornes(c) AdvancedPhysicsforYou,KeithJohnson,SimmoneHewett,SueHort,John

Miller.Publisher:nelsonthornes(d) IGCSEPhysics,TomDuncan,HeatherKennett,Publisher:HodderMurray(e) NotesfromMITOpenCourseware(http://ocw.mit.edu/)(f) Internet

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