B l o w i n g

S n o w

EXPERIMENT OUTLINE

Thepurposeoftheexperimentpresentedherewasto
measure the charge-to-mass ratioon an individual blow-
ingsnowparticle.Inhisfamousexperiment,Millikan
(1910)measuredthe chargeofsingle electronsfromthe
motionofoildropsmovinginaconstantelectricfield.
Camp (1977)used a variation on thistechnique to deter-
mine charge-to-mass ratios for falling snow crystals.Based
on theirmethods we designed the apparatus and experi-
ment described below to measure the the charge on drift-
ing particles.Snow particles were extractedfrom saltation
byadrifttrap.Particlesthatdidnotimpactthetrap
droppedvertically through a still air chamber containing a
constanthorizontalelectricfield.Adetectortriggered a
photographic imaging system that produced photographs
showingparticlepath and location atknown timeinter-
vals.Chargedparticlearedeflected horizontallybyan
amount proportional to their charge, with direction deter-
minedbythe charge sign.Photographs showing deflec-
tion both left and right would confirm our hypothesis that
positiveandnegativecharged particlesaretransported
simultaneouslyin saltation.The charge-to-mass ratio of
theparticlecan bedeterminedfromtheseimagesusing
equations derived in the next section.

EQUATIONS OF MOTION

A charged particle falling through still air, with a horizon-
tal electric field,is acted upon by the gravitational force,
an electrostatic force, and a drag force dueto air resistance
thatopposestheparticlesmotion.Ifthedirectionthe

particle travels isdefined by an angle q with the vertical
(figure 1), the equations that describe the particle's motion
are
F
E^-Fd^{sinq =m x..}
(1)

and

The magnitude of the electrostatic force is F_E= qE, where
E is the magnitude of the electric field and q is the charge
ontheparticle.Fornon-spherical particlestravelingat
low speed, the magnitudeof the drag forcecan be approxi-
mated as F_d= k(3pm )d_nv (McNown,et.al.,1951).Here k
denotes the shape factorof the particle,mis the dynamic
viscosity of air, d_nis the particle's nominal diameter, and v
is the velocity of the particle.Substitutingtheseexpresions
into equations (1) and (2) gives

qE
and
-k _x(3
pm)d_nvsinq =m x^..
..
mg-k_y(3 pm ) d_nv cosq=m y

(3)

(4)

(v)sinq and (v)cosq are the horizontal and vertical compo-
nents of particle velocity so that

qE
and
-k_x(3
pm)d_nx^.
=m x^..
...
mg-k_y(3 pm)d_ny=m y

(5)

(6)

Assumingtheparticlefallsatterminalvelocityv,the
vertical component of acceleration is zero, andthe ver^T
tical
componentofvelocityisconstant.Equation(6)then
becomes mg = k_y(3 pm )d_nv_Twhich can be rearranged as

₌ ⁽⁷⁾

m(3
pm)d_nv_T

mg-F_dcosq =my^..

(2)

Equation (8) expresses the motion of the particle in terms
of the variables E and v_T(which can be measured experi-
mentally) and the ratio q/m which we wish to determine.
Equation (8) is solved by separation of variable.Forbrev-
ity, we define thetwo constant expressions in equation (8)
asE(q/m)=aand (g/v_T)=b.Substitutingtheseexpres-
sions into equation (8),separating variables, and integrat-
ing both sides of the resulting expression gives

dx^·
[!]------
a - bx^{·=[!] dt}

T=---1n[a-bx^1·
b^]+c1

or

(9)

Weevaluate the constant of integration c₁by assuming the
x - component of velocityis very small when the particle
enterstheelectricfield.Attimet=0,X=0therefore
c₁ =ln[a]/b. Expression (9) becomes t = -(1/b) 1n[(a-bx)/a].
Exponentiating both sides this expression yields
1- e^{-b t}= (b/a) x, or

Figure 1: Free-body diagram of particle falling in air, subject to a

constant electrostatic force.

130

1-e^{- b t}=(--)---^bdx
adt

(10)