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SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
MILLIKAN’S Oil Drop Experiment
Millikan’s Oil Drop experiment was conducted at the turn of the 20th century. His goal
was to come up with a standard constant for the elementary charge. The data that he
used to find the value of the elementary charge is considered to be some of the most
accurate and meticulously obtained experimental data ever recorded.
SET-UP
A fine mist of oil was sprayed from an atomizer. Most of the droplets became
negatively charged as they picked up some small, unknown number of electrons as they
passed through the atomizers nozzle. Some of the drops then fell through a hole in the
top plate and drifted into the region between the two parallel plates between which a
variable electric field had been established.
CALCULATIONS
The space between the plates was lit from the side by an intense light and the drops
glistened when viewed through a telescope. Once a drop was located, the voltage
controlling the electric field (  ) was varied in order to slow down the drop's
descent. When the drop reached terminal velocity (mg = q  ) it was tracked through the
remainder of its fall and a ratio of mass per unit charge was recorded.

SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
Once the mass of the drop could be determined then the drop's electric charge could
mgr
be calculated from the recorded electric field strengths, (q = mg/  or q 
since
V
V

). By timing the drop's motion, its terminal velocity was calculated (d = vt). Using
r
equations for air resistance, Millikan was able to determine each drop's radius, and
volume. Using the density of oil and the volume, he was able to determine the mass of
each drop.
Once the mass of each drop was determined, Millikan and his graduate student H.
Fletcher, showed that the charges of the droplets always carried a whole number
multiple of a basic charge, qe = 1.592 x 10-19 C. Today, the accepted value for the
fundamental unit of charge is e = 1.602 x 10-19 C.
ANOTHER LOOK:
http://www.youtube.com/watch?v=XMfYHag7Liw&feature=related
SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
EX 1: In a Millikan type experiment, two horizontal plates are 2.5 cm apart. A latex
sphere, of mass 1.5 x 10-15 kg remains stationary when the potential difference
between the plates is 460V with the upper plate positive.
a)
Is the sphere charged negatively or positively?
b)
Calculate the magnitude of the charge?
c)
How many excess or deficit electrons does the sphere have?
HMWK: Pg. 362 #1-6
Pg. 364 #3,4
SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
Motion of Charged Particles in an Electric Field
Consider a small positive charge q2, with a very small mass, a distance r from a fixed
positive charge q1. q2 experiences an electrical force to the right and moves from
kq q
position A to position B. The magnitude of the electrical force is given by FE  12 2 .
r
By Newton’s second Law, we know that the particle will accelerate in the direction of the
force and since gravitational effects can be neglected Fnet  FE  ma .
+
+
+
_________r___________
q1
q2 at position A
q2 at position B
As the test charge (q2) moves from position A to position B, the distance from the
original charge increases yet the force decreases. With the decreasing force, the
acceleration of the test charge decreases as well.
Looking at the energies involved:
At position A:
EA 
kq1 q 2
rA
At position B:
EB 
kq1 q 2
 EK
rB
The conservation of energy law states that the energy before should be equal to the
energy after.
E before  E after
E A E B
kq1 q 2 kq1 q 2 mv 2


rA
rB
2
kqq q 2
 kq q
  1 2 
rA
 rB
 E E  E K
 mv 2


2

SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
EX 1:
SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
EX 2: An electron with an initial speed of 103m/s is aimed at an electron held stationary
1.0 x 10-3 m away. How close to the stationary electron will the moving electron
approach before it comes to a stop and reverses its direction? 3.4 x 10-4 m.
EX 3: A small particle of mass 1.0 x 10-5 kg and a charge of +1.5 x 10-5 C is released from
rest at position 1, which has a potential that is 12V higher than at position 2. What is
the speed at position 2? (6 m/s)
SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
Ex 4: An electron is fired horizontally at 2.5 x 106 m/s between two horizontal parallel
plates 7.5cm long. The magnitude of the electric field is 130 N/C. The plate separation is
great enough to allow the electron to escape. Edge effects and gravitation are
negligible. Find the velocity of the electron as it escapes from between the plates.
HMWK: Pg. 368 #2-5
Pg. 371 #2-5
SPH4U1 – FIELDS – L5 Milliken and The Motion of Charged Particles
ASSIGNMENT PROBLEMS
1. A proton with a charge of 1.60 x 10–19 C is shot from plate B toward plate A with a
speed of 1.5 x 106 m/s. (
d = 0.0030 m)
(a) What is the electric potential between the plates?
(b) What will the speed of the proton be just before it hits plate A?
2. In a Millikan-type experiment, two horizontal parallel plates are 3.5 cm apart. A
sphere of mass 4.2 x 10–17 kg remains stationary when the potential difference between
the plates is 5.00 V with the upper plate positive.
(a) Is the sphere positively or negatively charged? Explain.
(b) Calculate the magnitude of charge on the sphere.
(c) How much excess or deficit of electrons does the sphere have?
3. Two spheres are located 0.50 m from one another. Sphere A with a charge of –2.7 x
10–4 C, is fixed in position, but sphere B with a charge of –5.6 x 10–5 C is free to move.
Spheres A and B each have a mass of 1.3 x 10–2 kg. How fast is sphere B moving when it
reaches a distance of 0.95 m from sphere A? (Assume all distances are centre-to-centre.)
4. Two parallel plates labeled W and X are separated by 5.2 cm. The electric potential
between the plates is 150 V. An electron starts from rest at time tW and reaches plate X
at time tX. The electron continues through the opening and reaches point P at time tP.
(Remember: e = –1.6 x 10–19 C and the mass of an electron is 9.1 x 10–31 kg.)
(a)
Sketch the speed-time graph on the axes above.
(b)
Determine the velocity of the electron as it arrives at plate X.