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!!!!!!!!
4 3
! a ( "oil # "air )!!!
3
b = 6! a$
m=
-bv
s
d
mg
1.
2.
3.
+-qE
V
E =V /s
q = ne!?
With V=0, after a brief fall time the drop reaches terminal velocity v0 = d / t0 .
V is adjusted +-V I and v measured again by determining the time t+- to
move distance d.
The data can be used to show that charge is quantized and to determine the
fundamental charge q0 = e.
1
Solving First order DE
dv
= F(v)!!!!!!!!!!!!!!!!!!!!!!!!!!! F(v) =!"(mg + bv)
dt
v
t
dv
1
!#
= # dt
F(v)
m0
0
m
v
#
0
dv
"b
=
#0 dt
mg
m
(
+ v)
b
v
vo
t
t
"b
!!t
mg
"b
% mg (
m
ln(
+ v) !!=
!!t !!!!!!!!!!!!!!$!!!!!!v(t) =! '
(1
"
e
)
*)
&
b
m
b
0
mg
t >> 0!!!v0 =!
!!!terminal!!!velocity
b
v
2
Millikan Oil Drop Experiment (2)
d
d
qE =!mg + b! !!!!!!!!Equation!of motion!after!ter min al!velocity!reached.!v0 = !!!!!(1)
t
t0
1 ! E $
1
1 1
! mg $
! ±V / s $
! | V | /s $
=#
q
'
!!!=!!!
q
+!
!!!!!!!!(!!!!!
'
=
2!
&
#"
&
#"
&
#"
& q!!!!!!!!!!!!!!(2)!!!
t ± " b!d %
b!d %
b!d %
t0
t+ t'
b!d %
2
1
! mg $ 2 a ( )oil ' )air )
= '#
=!
g!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(3)
" b!d &% 9
t0
* !d
1)
2)
3)
4)
5)
6)
7)
8)
See data in Table 1.1 for your calculations.
Use Eq (3) t0 to find the average drop radius a for each case. You
will need this to find b in step 3).
Use Eq (2) to find q for each trial (1-12).
Assume fundamental charge e=qmin .
Determine n = q/qmin and round off n to the nearest integer.
Graph 1/t vs n (see Figure 1.4). How does this linear plot
show that q is quantized?
Determine the best value of the electron charge e = qmin from the 12 data
points (drop-1 and drop-2).
Values of ρ−oil and ρ-air are in the text.
3
4
5
6