Download Electron Charge to Mass Ratio

Physics 260 Calculus Physics II: E&M
Grist
Electron Charge to Mass Ratio
In this experiment you will measure e/m, the charge to mass ratio for the electron. It turns out
that if purely electric and magnetic effects are considered, then only the ratio e/m can be
found, not e nor m by itself. Not until 1911, in a classic experiment using other than purely
electrical effects, did Millikan measure the electron charge separately. Once that was
measured, the electron mass could be calculated since the ratio e/m was well known from
experiments like the one you will do today.
Theory
Electrons are emitted from a hot filament, accelerated through a potential difference, and
then bent into a circular path by means of a magnetic field. All of this is carried out in a large
glass tube, partially evacuated, but containing a small amount of mercury vapor. When some
of the electrons collide with mercury atoms light is emitted, and this allows us to visually
follow the electrons in their circular dance. The radius of the electron path is determined by
having the beam strike one of several pegs which are at known positions in the tube. The
magnetic filed is provided by placing the tube between two Helmholtz coils which provide a
very uniform field.
Distance Peg
Wire Filament
(perpendicular to page)
B (out)
5
4
3
2
1
Partially
Evacuated Tube
Anode
(or Plate)
Slit
Electron Path
Electrons emitted from the heated filament are accelerated toward a cylindrical plate (called
the anode) and emerge through a slit. These electrons have a kinetic energy of mv2/2 which
is equivalent to the change in potential energy eV between filament and anode.
1 m v2 = e V
2
(1 )
The moving electrons feel a magnetic force of magnitude
F= B e v
Electron Charge to Mass Ratio
(2 )
page 1
Physics 260 Calculus Physics II: E&M
Grist
if B is perpendicular to the electron path. This force causes the electrons to move in a circular
path of radius R, and we can write
2
F= B e v = m v
R
(3 )
Which leads easily to
e =
m
2 V
B
2
R
(4 )
2
The magnetic field is provided by two Helmholtz coils. These are two identical coils mounted
on a common axis and separated by a distance equal to the coil radius. This arrangement
produces a nearly uniform field over a large region between the coils.
I
Rc
B around point P
is fairly uniform
P
Rc
N turns
I
The field in this region is given by
B =
8 µo N I
1 2 5 Rc
(5 )
where
N = 72 is the number of turns in each coil,
I (to be measured) is the coil current in Amperes, and
Rc = 0.33 m is the average radius of the coils.
The Helmholtz coils are are tilted so that their axis is parallel to the earth’s magnetic field.
(This can be checked with a dip needle.) The current is sent through the coils in such a
Electron Charge to Mass Ratio
page 2
Physics 260 Calculus Physics II: E&M
Grist
direction that the Helmholtz field is directed opposite to that of the earth’s field. The current
through the coils is controlled by rheostat R2 and is read on ammeter A2 (see the circuit
diagram).
The accelerating voltage V is obtained from a regulated DC power supply. The exact voltage
is read on voltmeter V. The milliammeter monitors the plate (anode) current and need not be
recorded. The current to heat the filament is supplied by a DC power supply (6 V), controlled
by rheostat R1 and read on ammeter A1 (see the circuit diagrams).
Circuit Diagrams
Helmholtz Circuit
Coils
R2
A2 (0 - 3 A)
(0 - 5 ž)
12 V (Power Supply)
Filament Circuit
Anode
Anode Circuit
Anode
Filament
Filament
mA
S1
(0 - 10 A)
R1
A1
Regulated DC
Power Supply
(- 30 V)
(0 - 2.5 ž)
S2
V
(- 6 V)
Note the common ground connection on the filament and anode circuits.
Electron Charge to Mass Ratio
page 3
Physics 260 Calculus Physics II: E&M
Grist
Procedure
1.
Set up the anode, filament, and Helmholtz coil circuits as shown in the circuit diagrams
(last page). Switches S1 and S2 should be open initially.
I must check the wiring before you continue!
2.
Turn on the filament power supply and set for 6 V.
3.
Put all of R1 into the circuit and close switch S1. Slowly decrease R1 until the filament
current reaches 3 A (read on ammeter A1). You will see the filament glow after about a
minute.
4.
Close switch S2 . Set the regulated DC power supply B+ control so that the accelerating
voltage (read on V) is 30 V.
5.
Slowly decrease R1 to increase the filament current. At some point around 4.0 A a beam
will be obtained and the milliammeter will begin to show a plate current. Continue to
increase the filament current until the plate current reads about 3 – 5 mA. If the
milliammeter shows no plate current by the time the filament current reaches 4.5 A, turn
off the power supply and check with the instructor.
One student should monitor the milliammeter and immediately open S1 if
the plate current exceeds 10 mA.
6.
After you obtain a visible beam you will notice that it curves slightly due to the earth’s
magnetic field. Increase the current in the Helmholtz coils until the beam is straight. This
is accomplished by starting with all of R2 in the circuit and gradually reducing the
resistance. The field of the coils is now equal and opposite to the earth’s field. Record
this current at Io.
7.
Increase the current through the coils until the sharp outside edge of the beam strikes
the outside edge of peg #1. Record this current as I1. The outside edge is used because
it is determined by the electrons having the highest speed, corresponding to the
potential difference measured by the voltmeter.
8.
In a like manner determine and record the currents I2 … I5 required to cause the beam
to strike the outside edge of the other four pegs.
Electron Charge to Mass Ratio
page 4
Physics 260 Calculus Physics II: E&M
Grist
Calculations
1.
From each of the values I1 … I5 subtract the value of Io, to find the effective value of the
current to be used in Equation (5) to calculate the net field existing at the tube.
2.
For each peg, calculate e/m from Equation (4). The radius of the electron orbit R is
determined from the following data on the distance from the filament to the outside edge
of each peg. Note that these distances represent the diameters of the orbits, not the
radii.
4.
Peg
Distance to filament (m)
1
2
3
4
5
0.115
0.103
0.090
0.078
0.065
Calculate the average value of e/m and also the percent error from the known value.
Questions
1.
What would happen if the axis of the Helmholtz coils was not parallel to the earth’s
magnetic field.
2.
Derive Equation (5) for the field on the axis of the Helmholtz coils and exactly midway
between them. Note that the geometry of the coils is such that the separation of the coils
is equal to the average radius of either coil. Use the formula derived in class for the field
on the axis of a current loop, and the principle of superposition.
Electron Charge to Mass Ratio
page 5