45
EXPERIMENT
DrivingForceand Terminal
Velocity
To qnswerthe quesiion"ls there o smqllest
unii of electric chorge?" we must be oble
to work wifh ond meosure extremely smoll
chorges. We detect electric chorges through
the electricforcesexerted on chorged bodies.
To detect very smoll chorges, therefore, we
mustbe oble to hondle very smoll forces.The
weight ond other forces octing on bodies of
ordinory size qre so lorge thot electricforces
ore insignificqnt unlessthe chorge is greot;
therefore, very smoll obiects qre essentiql.
Useful obiects for this purPoseore the smoll
plostic spheresmode for colibroling electron
Figure 45.1 showsq few of them.
microscopes.
The spheresore rqrely neutrol; mostof ihem
cqrry o smoll electric chorge. We sholl qttempt to meosurethe chorge by meosuring
the electric forces octing on ihem.
The opporqtus is shown in Fig. 45.2. The
only criticol odiustment involvesposifioning
the light sourceso thqt the imoge of the bulb
fifoment is formed right ot the center of the 75
plotes. To odiust the light source, you c qn
hold q piece of poper verticolly over the
center of the plotes, tilt the light source so
thqt it shines on the pqper, ond slide t he
light-sourcetube bock ond forth until o cleor
imoge is formed on the poper. The filoment
of the light sourceshould be verticol.
PIug the wires from the plotes into the
connectors.CAUTION:The volioge is dongerously high; do not turn on the power supply
until you hove finished moking the connections.
The switch controls the chorge on the
plotes. ln the center position there is no
chorge; with the switch up, one plote is posilive, the oiher negotive; ond with the switch
down, the polorities ore reversed.
With the light turned on, squeezefhe bulb
to bring in o cloud of spheres,leoving the
switch centered. Whot do the spheres do?
(Noie thot everythingoppeors inverted when
you look through the microscope.)Are they
oll moving in the some direction? Are they
occeleroiing os they move ocrossthe field?
photographof a few
45.1 An electron-microscope
FTGURE
latex spheresof diameter1.8 microns.Thoseusedin the
experimentare a little smaller.
of the spheresin
FIGURE45.2 The jar containsa suspension
water. When you squeezethe bulb, a fine sprayof water
with many spheresis blown into the region between the
leavinga cloud of
plates.The water rapidlyevaporates,
spheresvisiblethroughthe microscopeas bright points.
ments or clumps of spheres; look for those
which move slowly in free foll.
Plot the doto for ony one sPhere on o
groph like thot in Fig. 45.4. How does ihe
velocity V+, observed when the driving force
is Fg * F", compore with the velocity when
grovity qlone is the driving force? How does
the velocity V-, observed when the driving
force is F"- Fufor the some sphere,compore
with the velocity when grovity olone is the
driving force?Whot is the shope of the groph
of velocity os q function of driving force for
one sphere?Whot is the shope of the groph
of velocity versusforce for your other spheres?
Whot con you conclude obout the relotion
between velocity ond driving force?
Veloc it y
(spoces,/second)
Force in Arbitrory Units
FIGURE45.4
77
76
Select o sphere ond meosureifs speed in two
ports of the field of view. Whot forces ore
octing on it?
How does chorging fhe plotes offect the
moiion of the spheres?Whot hoppens when
you reversethe direction of the electricfield?
Meqsureogoin the velocityof o sphere in two
poris of the field of view to see whether it is
occeleroting when on electric force is being
opplied. An explonqfion for the observed
moiion is thot the oir resislonceon thesetiny
spheresincreqsesropidly ond they very soon
move ot q consfqntterminol velocity with the
force of oir resistqnceequol ond opposite
to the driving force (which moy be groviiy
olone or grovity plus on electric force). ln
this experiment we wish to find the relqtion
between the terminql velocity ond the force
driving the sphere.
Y ou w i l l need three meosuremen ls on eoch
of qbout o dozen spheres. A set f or one
sphere consi sts of: o vel oci ty i n f r ee- f oll
under grovi i y ql one w i th no chorge on plot es;
o vel oci i y V + w here the el ectri cql f or ce is
i n the some di recti on qs the grovit ot ionol
force qnd the mogni tudes of the f or ces qdd
(Fg * F" ); qnd q vel oci ty V - w here t he electri col force i s opposi fe to the grovit ot ionol
force (F* - F" ). The di ogrqm of Fig. 45. 3
show s the forces i nvol ved.
For eqch sphere you w i l l theref or e hqve
three vel oci ti es: one for w hi ch th e dr iving
force i s grovi ty ol one; one, V + , w i th on electri c force odded; ond one, V -, w i th t he som e
el ectri c force subtrqcted.
Meqsure the vel oci ti es by ti mi ng t he m oti on over, sqy, ten spqces. Try to ovoid f r og-
(Fs- F.)
Fr ee Foll
I
FIGURE45.3
( Fs+ Fe)
EX P E R IM E N4T6
78 The Millikan Experiment
In the previousexperimentwe esioblished
thot the terminql velocity of the smoll plostic
spheresis direcily proportioriolto the driving
force octing on them. We sholl now use this
result to investigote whether the different
chorges oppeoring on difterenf spheresore
multiplesof o unit chorge. lf we ore coreful,
we ccrnchoosespheresof the some mossond
thus ensure thot the force of grovity is the
some on eoch. Furthermore,since we keep
ihe chorge on the plotesconstont,the electric
forceswill be proportionol to the chorgeson
the spheres,ond the difterencesin observed
velocity will be proportionol to differencesin
chorge on the spheres.
Set up the opporqtus os in the previous
experiment.CAUTION: Do not forget thot the
voltoge on ihe plotes is dongerous.Squeeze
the bulb to bring in o botch of spheres;then
throw the switch to chorge the plotes ond
sweep out the fosi-movingspheresthot hove
lorge chorges.
With the switch you cqn get two combinotions of forces: either Fe + Fe (electricforce
in the sqme direction qs grovity) or F* - F"
(electric force in the direction opposiie to
grovity). For eoch of ot leost l2lo 15 spheres
meosurethe velocity of the V+ run (Fe+ Fe)
qnd the V- run (F* - F").
lf you were sure thot oll test obiectswere
the some, you could onolyze your resultsby
moking o bor groph of the speeds qt o definite setting of the switch qnd looking for
evi dence thot certoi n speeds qre f qvor ed.
B ut you hove seen thot mony obi ect s in t he
fi el d of vi ew fol l extremel y sl ow l y or ver y
fost, ond i n Fi g. 45.1 (previ ous exper im ent )
tw o spheres qre show n cl u mped t oget her .
There i s l i ttl e doubt, therefore, thot fr ogm ent s
ond cl umps qre common, ond w e cqnnot be
sure l hqt ol l the spheres ore of i he som e size.
B y concel i ng out the effect of grovit y we
con mi ni mi ze errors resul ti ng f rom moss dif t er ences. W e know thot i he termi nol v elocit y is
proporti onol to the force. For eqch spher e
you hove o vel oci ty V + proporti onql t o Fs+ Fe
ond q second vel oci ty V - proport ionol t o
F" - F" . l f you subtroct V - from V +, t o whot
force i s i he resul ti ng vel oci ty propor t ionol?
C oul d you use these di fferences of velocit y
os o good meqsure of the chorge?
Y ou know thot the termi nol vel o ciiy of o
fl ot sheet of poper i s not the some o s t hof of
o sheet crumpl ed i nto o bql l . l f you or e observi ng o frogmenf or o cl ump, does it s veloci ty depend upon i ts si ze qnd shope?
H ow does thi s qffect i he vol i di ty of your
V + -V doi q os meosures of el ectri c chor ge?
Thi s di fti cul ty con be el i mi noted by using
onl y true spheres, ol l of the sqme moss. lf you
odd the vel oci ti es V + ond V -, l o whot f or ce
i s the sum proporti onol ? H ow cqn you use t his
resul t to sel ect q set of i denti col spher es?
There qre vori ous w oys i n w hi ch you could
onol yze these dqi q to l ook for evidence of
the di screteness of el ectri c chorge. O ne
si mpf e w oy i s to pl ot V + -V -, equol l y spoced
ol ong the hori zontol oxi s, i n i ncreqsing or der
on q bqr groph. W hot evi dence do you see
for the exi stence of o noturql uni t of chor ge?
W hot i s the smql l est number of cho r ges you
meosured?