Lab #
Name
Date
Lab Partner(s)__________________________________________________________________________________
Fundamental Charge and Charge-to-mass ratio of an electron
I.
INTRODUCTION
J.J. Thomson did experiments with cathode rays. By observing the motion of the rays in magnetic fields he was able to
show that the cathode rays were negatively charged particles, which we now know as the electron. In his experiments he
was able to measure the charge-to-mass ratio of the electron.
Robert Millikan did experiments in 1909 that determined the charge on an electron. He found that the charge was quantized and from his experiments he was able to calculate the fundamental "unit" of charge.
Combining these two experiments allowed scientist to know information about one of the building blocks of the atoms.
Other experiments were done that increased the knowledge of the fundamental particles.
II
EQUIPMENT LIST
+ e/m Apparatus
+ Power supplies for apparatus
+ Ammeter and Voltmeter
+ Ruler
+ Millikan Oil-drop simulation program
cess
III.
+ Computer w/ Internet ac-
BACKGROUND INFORMATION
A. e/m ratio
A large, helium-filled electron tube is mounted between a pair of Helmholtz coils. The tube contains an electron gun,
which generates a focused beam of electrons. A measured current is applied to the Helmholtz coils so that the magnitude
of the magnetic field within the electron tube can be calculated. A measured accelerating potential (V) is then applied to
the electron gun. The magnetic field (B) deflects the electron beam in a circular path with a radius (r) that is measured
using the illuminated mm scale. From these measured values, the charge-to-mass ratio of the electron is calculated.
When the electron is placed in a potential difference the electron will experience a change of motion. The potential is
set up so that the electron is essentially at rest and accelerated by the potential. By the work-energy theorem, the potential does work given by W = Vq. This will change the kinetic energy of the electron, ΔK = Δ( 1/2mv2). When the electron enters a uniform magnetic field that is perpendicular to the electron's velocity, the electron will experience a centripetal force that causes the circular motion of the electron. (qvB = mv2/r). Combining this allows one to solve for the
charge-to-mass ratio of the electron by the equation.
. The Helmholtz coils used in the apparatus produces a
uniform magnetic field in the region between the coils. The magnetic field is dependent on the physical configuration
(radius of the coils and distance apart) and the current in the wires of the coils. For the apparatus we have,
, where I is the current, N is the number of coils (130), and R is the radius of the coils.
B. oil drop
A schematic of the oil drop is shown at the web site. In the experiment, oil droplets are sprayed into a chamber and allowed to fall into a region where a voltage could be applied to create a uniform electric field. The electric field could be
adjusted to balance the gravitational force on the droplet. In the equilibrium condition, mg = qE. When the electric
field and mass are known, the q of the mass can be computed. In the experiment, Millikan and his associates did not
know the size of the droplets nor the charge (value or sign) on the droplets. His apparatus had to accommodate these
variations and they had to have a technique to get that data. In the experiment, he was able to measure the terminal
speed of the droplets as they fell. The terminal velocity occurred when the droplets dropped at constant speed due to the
air resistance balancing the gravitational force. The air resistance force depends on the density, volume, (or mass) and
shape of the falling object and the density of the medium through which the mass is falling.
IV.
A.
B.
C.
A.
B.
EXPERIMENTAL PROCEDURE
e/m ratio
Set up the circuit as directed by the instructor.
Select a voltage and current that will give a measurable radius of the electron orbit. Record data.
Repeat part B for four more voltage and current values.
oil drop
Open the Internet access on the laptops.
Go to web site:
http://webphysics.davidson.edu/applets/pqp_preview/contents/pqp_errata/cd_errata_fixes/section4_5.html
C.
Read and follow the directions for acquiring a droplet and stopping its motion with the controls.
D.
Stop droplets for four more mass or charge configurations.
V.
DATA
e/m ratio
Record the voltages, current, radius of the coil and radius electron's path for each trial
oil drop
Record distance and time for terminal speed, voltage for stopping motion for each trial
VI.
D.
E.
F.
CALCULATIONS
e/m ratio
Determine the magnetic field for each trial
Calculate the charge to mass ratio with the particle.
Calculate the percent error between the theoretical and experimental values of e/m for the electron.
oil drop
Determine the electric field for each trial
Calculate the terminal speed and then the mass of each particle
Compute the charge on each droplet
VII.
1.
2.
3.
4.
CONCLUSION/QUESTIONS
What are the possible sources of error in the e/m experiment?
Will the earth's magnetic field by a factor in e/m experiment? Explain.
What simplifications are made in the oil drop experiment?
Using your data from the two experiments, calculate the mass of the electron..
A.
B.
C.