Millikan Oil Drop Experiment

Millikan Oil Drop Experiment
•Millikan's apparatus first showed that charge q = ne was quantized.
•Charged oil droplets were balanced in between electrostatic plates.
•The net force on a falling oil drop is due to the acceleration of gravity mg, a retarding
drag force -bv of air resistance, and elecrostatic force qE.
F = ma = mg ! bv!±!qE!!!!!!!!
s
-bv
mg
+-qE
d
V
m = 4 3 !a3 (" oil
# " air
)!!!
b = 6!a$
E = V / s
q = ne!?
1. With V=0, after a brief fall time the drop reaches terminal velocity v 0 = d / t 0 .
2. V is adjusted +-V I and v measured again by determining the time t +- to
move distance d.
3. The data can be used to show that charge is quantized and to determine the
fundamental charge q 0 = e.
1

Solving First order DE
m dv
dt
!
v
#
0
v
#
0
= F(v)!!!!!!!!!!!!!!!!!!!!!!!!!!! F(v) =!"(mg + bv)
dv
F(v) = 1 t
m
# dt
0
dv
( mg = "b
t
b + v) m
# dt
0
v
ln( mg
b + v) !!= "b
0
m !!t!!!!!!!!!!!!!!$!!!!!!v(t) =! % mg (
&
'
b )
* (1" e
t >> 0!!!v 0
=! mg
b !!!terminal!!!velocity
"b
m !!t )
v
t
v o
2

Millikan Oil Drop Experiment (2)
qE =!mg + b! d t !!!!!!!!Equation!of motion!after!ter minal!velocity!reached.!v 0
= d t 0
!!!!!(1)
1
t ±
=
!
"
#
E $ !
b!d %
& q '
mg $ ! ±V / s$
"
#
b!d %
& !!!=!!!
"
#
b!d %
& q +! 1 !!!!!!!!(!!!!! 1 ' 1 ! | V | /s$
= 2!
t 0
t +
t '
"
#
b!d %
& q!!!!!!!!!!!!!!(2)!!!
1 !
= '
mg $
t 0
"
#
b!d %
& =! 2 9
a 2 () oil
' ) air
)
g!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(3)
*!d
1) See data in Table 1.1 for your calculations.
2) Use Eq (3) t 0 to find the average drop radius a for each case. You
will need this to find b in step 3).
3) Use Eq (2) to find q for each trial (1-12).
4) Assume fundamental charge e=q min .
5) Determine n = q/q min and round off n to the nearest integer.
6) Graph 1/t vs n (see Figure 1.4). How does this linear plot
show that q is quantized?
7) Determine the best value of the electron charge e = q min from the 12 data
points (drop-1 and drop-2).
8) Values of ρ−oil and ρ-air are in the text.
3