Download Millikan`s Experiment and Motion of Charges Lesson

The Millikan Oil Drop
Experiment
& Elementary Charge
Scientists wondered …
Does there exist in
nature a smallest
unit of charge?
If so, what is the
magnitude of this
“elementary charge”?
The Millikan Oil-Drop Experiment
FE = FG
qe = mg
q = mgr
∆Vb
since e = ∆V
r
where DVb is the
balancing value
b/w the plates
q DVb = mg
r
(-)
negatively
charged plate
FE
+
e
Fg
Vb
(+)
http://www.youtube.com/watch?v=XMfYHag7Liw
r
positively
charged plate
Determining the Elementary Charge
q = mgr
DVb
The Elementary
Charge
e = 1.602x10-19C
(-)
negatively
charged plate
FE
+
Fg
q = Ne
where N = # of
excess/deficit of
electrons
e
Vb
(+)
r
positively
charged plate
Example 1
Two parallel plates are placed 1.5cm apart with a
potential difference of 275V between them. The upper
plate is negative. An oil drop of mass 4.5x10-15kg is
balanced inbetween the plates similar to Millikan’s
experiment.
a) Is the drop charged positively or negatively?
b) What is the charge magnitude on the drop?
c) How many excess/deficit electrons does the drop
possess?
Limitations
Millikan accurately calculated “e”.
But his experiment did not adequately
describe the motion of charged particles
(due to the presence of air resistance).
Instantaneous
Acceleration
a = FE
m
q2
FE
+
r1
q1
+
r2
 Acceleration of the charge will decrease
because as r↑, FE↓
Conservation of Energy
ET = EE + EK
q2
FE
+
r1
ET’ = EE‘ + EK’
q1
+
r2
 Total Energy of the charge remains constant
because as EE decreases, EK increases
any change in a particle’s electric potential energy results in
a corresponding change to its kinetic energy when moving
in an electric field (and ignoring gravitational effects)
Special Case
Recall that parallel plates are a special case
where e is uniform and constant …
Therefore Electric Force is constant since
FE = qe
and so is acceleration, since
a = FE
m
∴ a charged particle in a uniform field moves w/
uniform acceleration
Special Case
Therefore, between two parallel plates :
- DEE = DEK
-qDV = ½ mn 2
If n  10% the speed of light (v~ 3.00x107m/s) then the answer is not valid
 relativistic effects increase the mass
Example 2
An electron is fired horizontally at 2.5 x 106 m/s
between two horizontal parallel plates 7.5 cm 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 gravitational
forces are negligible. Find the velocity of the
electron as it escapes from between the plates.
Example 1 - EXTRA
A particle accelerator uses two parallel plates to
accelerate a helium nucleus, or a particle, toward
a Cesium atom in order to split it. The potential
difference across the plates is 50,000V. With what
speed does the a particle hit the Cs atom if it starts
at rest? Is this answer valid?
ma= 6.6x10-27 kg
qa = 2e = 3.204x10-19 C
Example 2 - EXTRA
A stray, stationary proton finds itself 450nm
from a gold nucleus. How fast will it be
travelling when it is 15mm away?
Au
+
qp
qp
+
+
450nm
15mm
Example 3 - EXTRA
A small sphere with a charge of 750mC and a mass
of 25mg is located midway between two charged
plates separated by 40cm with a voltage of 200V.
The charge is pulled slowly upward by a string until
it reaches the positive plate and is then released.
a) How much work does the string do on the
sphere?
b) What average force does the string exert?
c) With what speed does the sphere reach the
negative plate?