PHYSICS 124 EXPERIMENT NO. 5PHYSICS 124 EXPERIMENT NO. 5MEASUREMENT OF THE CHARGE/MASS RATIOMEASUREMENT OF THE CHARGE/MASS RATIO

FOR ELECTRIONSFOR ELECTRIONS

Goal Goal Measure the electron charge to mass ratio.Measure the electron charge to mass ratio.

EquipmentEquipment

There are two different setups used in this experiment:There are two different setups used in this experiment:

Setup ASetup A

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.

Accelerating voltage for electron gun Current for Helmholtz coils

Helmholtz coilsHelmholtz coilsElectron gun and acceleration stage

Setup BSetup B

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.

Low voltage power supply

Current meter

Voltmeter meter

Heating voltage

Wires

Helmhotz coils

Electron gun and acceleration stage

OverviewOverview

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:

(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:

(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:

(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:

(6)

ProcedureProcedure

Setup ASetup 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. The 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).

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)

Setup B: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)

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)

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 plug-in. 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:

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?

Your write-up must include:

1) Derivation of equation (6).2) Answers to questions 1 and 2.3) Your value for e/m with error calculated from your 5 measurements.4) Does your answer agree within error to the accepted value of 1.76 1011C/kg?