Download 124-04_EM_of_electron

PHYSICS 124 EXPERIMENT NO. 5
MEASUREMENT OF THE CHARGE/MASS RATIO
FOR ELECTRIONS
Goal Measure the electron charge to mass ratio.
Equipment
There are two different setups used in this experiment:
Setup A
Helmholtz coils
Electron gun and
acceleration stage
Accelerating voltage
for electron gun
Current for Helmholtz coils
e/m of electron apparatus:
Including electron gun, acceleration stage, helmholtz coils, power supplies, voltage and
current meters. In this setup all controls are integrated and only acceleration voltage and
current through the helmholtz coils are adjustable. The Helmholtz coil has 130 loops.
Setup B
Helmhotz coils
Low voltage
power supply
Current meter
Electron gun and
acceleration stage
Heating voltage
Voltmeter meter
Wires
e/m experimental apparatus (referred to as “Helmholz coils”):
including electron gun, acceleration stage, Helmholtz coils. Power needs to be supplied
externally. The Helmholtz coil has 130 loops.
Low Voltage AC/DC power supply:
Supplies current for Helmholtz coils and is equipped with current meter.
High voltage supply:
Provides heating voltage for electron gun and electron acceleration voltage, as well as a
meter to read the acceleration voltage.
Wires:
To connect power supplies to experimental apparatus.
Overview
A charged particle moving in a magnetic field (B) with a velocity (v) experiences a force.
Magnitude and direction are given by the equation Fm = q v×B, (where F, v and B are
vectors and v×B is a vector cross product). In the experiment you observe electrons with
charge -e moving perpendicular to a magnetic field, so the cross product simplifies to a
product of the magnitudes of the vectors:
Fm = -e vB
(1)
where the direction of Fm is determined by the “right hand rule”. Since the electrons are
moving in a circle, they must be experiencing a centripetal force of magnitude
Fc = mv2/R
(2)
where m is the mass of the electron, v is its velocity, and R is the radius of the circle.
Since the only force acting on the electrons is that caused by the magnetic field, Fm = Fc,
so equations 1 and 2 can be combined to give:
e


m Br
(3)
Therefore e/m of the electron can be determined from the velocity of the electrons, the
magnetic field, and the radius of the circling electron beams.
In your setup the electrons are accelerated though an electrical potential V, gaining
kinetic energy. Because before acceleration the potential energy of the electrons is eV the
velocity can be calculated from the electrical potential using energy conservation:

2eV
m
(4)
The magnetic field in the setup is produced by a pair of Helmholtz coils. The magnetic
field near the center axis through the pair of Helmholtz coils is given by the equation:
B
N 0 I
5 43 2 a
(5)
Where a is the radius of the coils, N number of loop on each coil, I the current through
the coils and 0 is the permeability constant 4×10-7 H/m. (The derivation of (5) can be
found in your textbook.)
Combining equations (3), (4), and (5) gives for the e/m of the electron:
e 2(5 4)3 V a 2

m  N 0 I  2 r 2
(6)
Procedure
Setup A
1) Turn the power on. In the display labeled “COIL CURRENT” there will be a
countdown of how long it will take the beam to start.
2) When the countdown is finished you should have a voltage and current reading
displayed if you do not see a beam, turn the voltage knob (on the left) up until it is
about 150V and turn the current knob (on the right) to about 1A.
3) You should now see the glowing beam created by the electrons. If everything is
already working it should be moving in a circle and coming back around and
hitting the back side of where it started. If this is not the case then
a. If your beam is running straight into the side of the glass without bending,
increase the current that you read off of the low voltage supply, or lower
the voltage read off of the high voltage supply.
b. If the beam is spiraling instead of just moving in a circle, gently turn the
bulb forwards or backwards until it is moving in a circle.
4) Now that you have a nice circular beam you need to record the voltage, the
current and the radius. To measure the radius, there is a measuring stick inside of
the bulb. If your beam is moving properly it should be moving through this,
lighting it up. The number that you read off of it is the diameter in cm and you
need to divide this by two to get the radius and then record the radius in your lab
book. Remember to include decimal places, not just to write down a diameter of
10 if the beam hits halfway between 10 and 11.
5) Increase the voltage on the high voltage source and repeat the steps in 4) then
increase the voltage once more and repeat the steps in 4). You should have 3
different voltage readings.
6) Now increase the current on the low voltage source and repeat the steps in 4) then
increase the current once more and repeat the steps in 4). You should have 2
additional readings with different currents.
Setup B:
There are three pieces to this set-up which will be referred to as the Helmholtz coils, the
low voltage box and the high voltage box.
1) Turn on the low and high voltage boxes and adjust them so that the high voltage
box has at least a 100V reading and the low voltage box has a 1A reading. If you
can’t adjust the current on the low voltage box try turning the knob on the
Helmholtz box labeled “CURRENT ADJ”.
2) WAIT. The voltage supply needs to heat electrons off and if you raise your hand
immediately and say “Mine isn’t working” it is like when you try to boil water
and complaining that it doesn’t work at soon as you turn on the stove. You are
going to be boiling off electrons and it may take a couple of minutes.
3) You should now see the glowing beam created by the electrons. If everything is
already working it should be moving in a circle and coming back around and
hitting the back side of where it started. If this is not the case then
a) If your beam is running strait into the side of the glass without bending,
increase the current that you read off of the low voltage supply, or lower
the voltage read off of the high voltage supply.
b) If the beam is spiraling instead of just moving in a circle, gently turn the
bulb clockwise or counterclockwise until it is moving in a circle.
4) Now that you have a nice circular beam you need to record the voltage from the
high voltage source, the current from the low voltage source and the radius of the
beam. To measure the radius of the beam you need to line up the movable pieces
on the ruler with the edges of the beam. To do this you need to look
perpendicular to the ruler and line up each side separately then read off the
difference (in cm and not inches) which is the value of the diameter. Divide this
by two to get the radius and record it in your notebook.
5) Increase the voltage on the high voltage source and repeat the steps in 4) then
increase the voltage once more and repeat the steps in 4). You should have 3
different voltage readings.
6) Now increase the current on the low voltage source and repeat the steps in 4) then
increase the current once more and repeat the steps in 4). You should have 2
additional readings with different currents.
This section should only be followed if your apparatus is not set-up for you. Do not
take out wires unless your TA o.k.'s it.
The “Low voltage AC/DC Power Supply” box should be hooked up to the wire
connections at the far left of the Helmholtz coil box. The wires should not be plugged
into the part that is AC on the right of the low voltage supply box, but to the black and
red plug-ins on the left side of the box that has 0 – 24.
The other power supply box that has a high voltage marker on it should have a red
wire plugged in directly below the high voltage mark and that wire should be plugged
into the rightmost red plug in on the Helmholtz box marked electrodes. Then a black
wire should be plugged into the high voltage box directly left of the red wire and in the
Helmholtz box it should be plugged in directly below the red wire in the electrodes plugin. For the last two wires plug the red one into the rightmost slot in the high voltage
source in the section marked AC and also into the top rightmost part of the Helmholtz
box marked heater. Then the black cord should be plugged in just left of the red wire in
the high voltage box and just below the red wire in the Helmholtz box.
Write-Up:
Derive Equation (6)
Q1: How does the radius of the beam change when you increase the voltage and
why?
Q2: How does the radius of the beam change when you increase the current and
why?
Q3: What is your value for e/m (with error!) calculated from your 5 measurements?
Does it agree within error to the accepted value of 1.76*1011 C/kg?
Your write-up must include:
1) Derivation of equation (6).
2) Answers to questions
3) Your calculation of e/m and comparison to known value