Experiment 7: Charge to Mass Ratio For the Electron
Shock hazard: There will be uninsulated exposed connections at high voltage. The possible current
is limited to 3 mA, so it won't kill you, but try to avoid getting an unpleasant zap.
Part One: Sign of the electron’s charge.
You will observe whether electrons are positive or negative. A beam of electrons in an evacuated
glass bulb is shot across a screen coated with a material that glows where electrons hit it. There is a
magnetic field from a set of Helmholtz coils just outside the tube, whose direction is observed with
a compass. From the electron’s direction of motion and the direction of the field, it is determined
whether a positive or negative value for q makes q ⃑ ⃑⃑ match the observed direction of the force.
1. Connect the tube to the power
supply as shown. (Yours may not look
exactly like the picture.) Bear in mind
that the tube is fragile. The 6 V AC
heats the filament which is the source of
the electrons. (Do not connect to 12 V.)
The high voltage between the filament
and the anode accelerates the electrons.
2. Connect a second circuit from the 0 16 V DC power supply to the coils as shown. Use a digital
ammeter, on a scale suitable for around an amp. Obtain the
instructor's approval.
3. Turn on the tube's power supply, set for between 2000 and
5000 V. The blue line you see is the beam's path. Send some current through the coils. If there is
little effect on the beam, their fields are canceling not adding; switch the wires on one of them.
4. Observe whether the beam is positive or negative:
a. To see the direction of the field, ⃑⃑, hold a compass just outside the tube, in front of the
center part of the screen.
b. Using arrows, dots and x’s, draw a diagram showing, as you look at the screen:
- the direction of ⃑ when the electrons first enter the screen.
- the direction of ⃑⃑.
- the direction of ⃑ ⃑⃑.
- the direction of the observed force.
c. In your conclusion, state whether the direction of the force you saw indicates a positive or
⃑⃑. Based on the directions of ⃑⃑ and ⃑
⃑⃑, is q a
negative charge for the beam. (⃑⃑ = q ⃑
positive number or a negative number?)
Part Two: e/m
This is a modified version of J. J. Thomson’s 1897 experiment in which he discovered the electron.
(The experiment showed “cathode rays” to be a stream of particles, each with the same charge to
mass ratio, which he measured. e and m were not known individually until Robert Millikan
measured e in 1909.)
Notation: v = velocity, V = voltage
In the same tube, the magnetic field makes the beam follow a circular path. The magnetic force on
an electron, q v B, provides a centripetal force, m v2/r. Setting these equal and doing some algebra
gives a formula for q/m in terms of v, B and r. Show the details when you write your discussion.
Finding q/m, then, amounts to finding, v, B, and r: The speed, v, depends on the voltage used to
accelerate the electrons; the higher the voltage, the faster they go. You find B from the current in
the coils and their dimensions. The radius of the beam's circular path, r, comes from observing the
beam's path as it curves across the luminescent screen in the tube.
PROCEDURE:
1. Measure the coils’ diameter D and separation s. Side to
side, as shown, is the same as center to center, and is easier
to measure. They are not exactly parallel, so measure s on
both sides and average. They can be moved a little, so
measure s last when you will not be touching them again.
Use dividers because the tube is in the way of a ruler.
2. Turn on the tube, leave the field off. Around x = 8 or 9, notice where the x axis is
relative to the beam. In the example at left, the bottom of the beam is on the axis.
That would mean y values in step 3 should be read from the bottom of the beam.
Or, if the center of the beam is on the axis with the field off, read y from the center.
3. Turn on the magnetic field. From the centimeter grid, record the x and y coordinates of a point
on the beam, somewhere around x = 8 or x = 9 cm. (The equation for B is actually only valid near
the center of the screen. If you use a point too far to the right, the beam is just entering this part of
the field when you stop looking at it.) Be accurate to the nearest millimeter. y should be 1 cm at the
very least to minimize the effect of measurement errors. More is better.
4. The screens were not positioned accurately in many of these tubes. Correct x by the amount
shown on the tag on your tube.
5. Repeat for a total of three trials, using different combinations of V and I.
CALCULATIONS:
1. From your formula sheet, the magnetic field of a flat coil is
B = N μoI R2
2 (R2 + x2)3/2
Multiply by 2 because there are two coils. Substitute x = s/2 and R = D/2. The result is:
B=(
(
)
)I
N is the number of turns (printed on each coil) and I is current. (A large source of error is that this
equation is actually only valid on the axis of the coils; B varies somewhat between different parts of
the screen. A better setup would use larger coils for a more uniform field.)
Put in numbers for everything but I, and simplify into the form B = (constant)I. Show the details in
the space provided. Then, use this result to find B for each trial.
2. For each trial, calculate the radius of the beam’s path: The + plate of the electron gun, where the
electrons enter the magnetic field, is at the point x = 0, y = 0. If the electron beam passes through
the later point (x,y), we have from the Pythagorean theorem:
r2 = (r-y)2 + x2
r2 = r2 - 2ry + y2 + x2
2ry = x2 + y2
r = x2 + y2
2y
3. Get a formula for the electrons’ speed: As an electron is accelerated through the gun, the
potential energy it has on one side of the gun equals the kinetic energy it has on the other. In the
space provided, solve this conservation of energy equation for the electron's speed WITHOUT
FILLING IN NUMBERS YET. (The usual mistake is to look up q and m and calculate v from
them. q/m is what you've trying to measure; assuming values for q and m instead of treating them
as unknowns is circular reasoning.)
4. Substitute this into the equation you derived earlier (from q v B = m v2/r) to eliminate v. Square
both sides and simplify to obtain a formula for q/m. Use the result to find q/m for each trial.
5.Average your three values. Assume the result has a 20% uncertainty, primarily due to the
nonuniformity of the magnetic field.
CONCLUSION:
Divide the accepted e by the accepted m and compare to your results.
The write-ups for this lab seem particularly prone to people telling how to connect the wires, which
meters to read, and which equations to use, without ever mentioning how the experiment works. As
usual, I want to know what you did more than the details of how you did it. Completely describe
the line of reasoning that leads from your measurements to e/m.
PHY 132
Report on Experiment 7: e/m
Part One:
Part two:
D = _____________ s = _____________
B=(
Show how you got the number in the parentheses:
Trial
1
V
I
x
Corrected
x
)I
y
B
r
q/m
2
3
average q/m = ______________ ± ______________
Calculations of r’s:
Show how to obtain formula for q/m on the back.
Accepted e = _____________ Accepted m = _____________ Accepted e/m = _____________