SP212 Lab: Sixà Magnetic Force
Version: February 24, 2015
Physics II
Lab 6
SP212
MagneticForce
I. Discussion
A. Electronsaremadeavailablefortheexperiment:Insidethegridisa
heatingelement.Wecan'treadilyseetheheatingelementuntilthe
equipmentisturnedon,whenapowersupplyinsidetheequipment
providesavoltageacrosstheheatingelement.Theheatingelementthen
becomeshotandglows,muchlikethefilamentinalightbulb.Whenthe
heatingelementishot,wecanseethelightitproduces.Thefunctionof
theheatingelementistoraisethecathodetoahightemperature,giving
someoftheelectronsonthecathodeenoughenergytoescape(i.e.,some
electrons"boiloff"thecathode.)
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SP212 Lab: Sixà Magnetic Force
Version: February 24, 2015
B. The electrons are then accelerated between the cathode and the anode: A large
potential difference (voltage, Vaccel) is established between the cathode and the
anode. Most of the "boiled off" electrons collide with the grid. However, a few
electrons are going in the right direction and are accelerated through a hole in the
grid toward the anode. A fortunate few of these electrons actually pass through
another hole in the anode, forming the electron beam that we will study. Those
electrons that escape to form our electron beam will have a velocity that we can
calculate. In summary, we have electrons initially moving downward in the glass
tube with a speed we can calculate!
1 2
2(e)(Vaccel )
mv = qVaccel è v =
2
m
C. The electron beam is made observable: If the tube were at atmospheric pressure, the
electrons would not travel far because of collisions with the air molecules. For this
reason, most of the air has been removed. However, the path of the electrons is still
not observable even with the air removed. To make the "trail" of electrons
observable, low-pressure helium gas exists inside the tube. The helium enables us to
see the path of the electrons because a helium atom fluoresces (emits bluish light)
when an electron collides with it.
D. The electron beam is bent into a circle: A magnetic field causes the electrons to travel
in a circle once they exit the metal cylinder. This magnetic field is produced by an
electric current in a large set of coils outside the tube. There are two sets of circular
coils of radius R that are separated from each other by the distance R. Coils in this
configuration are known as Helmholtz coils. The special characteristic of Helmholtz
coils is that they produce a relatively uniform magnetic field near the center of the
configuration. Our electron beam will be located near the center of the coil
configuration in the uniform magnetic field.
r=
mv
eB
Note: The numbers on the bar indicate the beam diameter in centimeters (not the radius!).
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SP212 Lab: Sixà Magnetic Force
Version: February 24, 2015
II. TurninyourPre-lab/homeworkproblemifassigned.
III.Procedure
A. PreliminaryMeasurements
1. Valuesofthefundamentalphysicalconstantse,me,andµ0have
beenenteredforyouintothespreadsheettemplateforthis
exercise.NotethatI’veenteredtheirvaluesaccuratelyto9
significantdigits.Therearesomeuncertainties,buttheyare
sosmallthattheywillnotaffectyouruncertaintycalculations
verymuch,andwemaytreatthesequantitiesasexactforthe
purposesofthisexercise.
2. Youwillneedtomeasuretheaveragediameterofyour
Helmholtz(Hh)coilsandentertheresultinyourspreadsheet.
Themanufacturer’sinstructionmanualstatesthateachcoilis
madewith132turnsofwire.Themagneticfieldnearthe
centeroftheHhcoilsisproportionaltothecurrentflowing
throughthem;theproportionalityconstantis
[8*N*µ0]/[R*sqrt(125)].
B ≅[
8N µ0
]*i è B ≅ [constant]*i 125 R
WewilllearnmoreaboutthisinCH-29,ifyouhaven’talready.
Note: R is the radius (and separation) of the Helmholtz coils. i. Calculatethisproportionalityconstantvalueandenterit
intheappropriatecellinyourspreadsheet,alongwithits
uncertainty.
ii. Discussion:Inaparagraphconsistingofafewsentences,
describehowyoumeasuredtheaveragevalueofthe
diameterofyourHhcoils.
Please follow the instructions carefully. The equipment that we are about to use is very
expensive.
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SP212 Lab: Sixà Magnetic Force
Version: February 24, 2015
B. FirstExperimentalRun:Vaccel=200Volts.
1. Turn on the power switch to the equipment. The unit will do a 30 second
self-test and will energize the filament. The displays will stabilize and
read "000";iftheydon’tbothsteadyoutatzeroinlessthanaminute,let
yourinstructorknow. DO NOT TAKE DATA FOR AT LEAST 5 MINUTES.
2. Aftertheybothsteadyoutatzero,turntheacceleratingvoltageupto200
V,andtheHhcurrentto1.6Amperes.Youshouldseeaneerieblue-green
electronbeambentintoafullcircle;thisshouldgetbrighterforabout5
minutes.Afteryourinstrumentisfullywarmedup,youmaybegintaking
data.
3. Withtheacceleratingpotentialsetat200V(theuncertaintyisoneVolt),
gentlychangetheHhcoilcurrentuntilthediameteroftheelectron
trajectoryis11.0cm,or0.11m.Recordthediameterandthecurrent
requiredtobendthebeamtothisdiameter.Similarly,recordthecurrents
requiredtobendthebeamintodiametersof10,9,8,7,6,and5cm.
4. Youmaywishtocranktheacceleratingvoltageup,to300Vandtakethe
dataforPartCatthistime,beforereturningtothecalculationsdescribed
inthenextparagraph.
5. Calculations:
i. Fromtheorbitaldiameter,calculatetheorbitalradius.
ii. FromtheHhcoilcurrent,calculatethemagneticfieldusingthe
proportionalityconstantyoucalculatedinPartA.(Don’tforgetto
useabsoluteaddressing!)
iii. Onceyou’vecalculatedB,itiseasytocalculatethemagneticforce.
iv. Next,calculatethecentripetalforcerequiredtobendthebeaminto
theobservedradius,mv2/r:Youalreadyhavetheelectrons’KE,
whichismv2/2;multiplythatby2anddividebyr,andyou’vegot
her.
v. Thencalculatethe%differencebetweenyourmagneticand
requiredforces.Inthelastcolumn,calculatethevalueof
2*Vaccel/r2B2;asyousawfromthehomeworkproblem,thisshould
beequaltothecharge-to-massratiofortheelectron,calculatedin
PartA.
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SP212 Lab: Sixà Magnetic Force
Version: February 24, 2015
C. SecondExperimentalRun:Vaccel=300Volts
1. RepeatPartIII.BwithanacceleratingpotentialofVaccel=300V.
2. Discussion:DiscussionforpartsBandC:Doyourresultsshowthatthe
magneticforceactsasacentripetalforceandbendstheelectrons’
trajectoriesintocircles?Doesyourexperimentalvaluefortheratioe/m
agreewiththevaluecalculatedfromthewell-knownphysicalconstants?
D. LabReporttohandin:
1. PreliminaryDataspreadsheet,withdiscussionsfrompartA,andfrom
partsBandC.
2. Datasheetforfirstrun,withVaccel=200V.
3. Datasheetforsecondrun,withVaccel=300V.
Don’tforgetuncertainties,units,annotationsanddiscussions.
IV.
Clean-Up
A. GoldenRule:“Dountoothersasyoudesirethemtodountoyou.”
ThisappliesasmuchhereinthelabasitdoesintheFleet.AsfutureNavalOfficers,
howcanyouexpectyourenlistedsailorstomaintainacleanworkareaifyour
stateroom,workareas,messarea,etcisa“pigsty?”Soasofficersitisimperativethat
wecleanupafterourselvesnotonlytofollowtheGoldenRule,butalsotoleadby
examplefortheenlistedpersonnelunderourcharge.
1. EndofLabCheckout:Beforeleavingthelaboratory,pleasetidyupthe
equipmentattheworkstationandquitallrunningsoftware.
2. Thelabstationshouldbeinbetterconditionthanwhenyouarrivedandmore
importantly,shouldbeofanappearancethatyouwouldbePROUDtoshowto
yourlegalguardiansduringa“ParentsWeekend.”
3. Haveyourinstructorinspectyourlabstationandreceivetheirpermissionto
leavetheLabRoom.
4. YouSHALLfollowthisprocedureduringeverylabforSP212!
ManythankstoDr.HuddleandDr.FontanellafortheirassistanceinproducingthisLaboratory
procedure;specificreferencescanbesuppliedonrequest.LCDRTimothyShivok
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