__
Objective:__

The objective of this experiment is to measure the mass of an electron by using electric and magnetic fields.

__Equipment:__

Tuning-eye vacuum tube, high-voltage dc source, two 12 V dc power supplies, two multi-meters, a few cylindrical objects of circular cross-section (of small diameters such as pencils or plastic rods), a solenoid (with an inside diameter greater than the outside diameter of the tuning-eye tube), connecting wires, and a calculator

__
Theory:__

It is possible to use an **electric field**
perpendicular to a **magnetic field** in order to measure the **mass of an
electron** knowing that the electronic charge is e**
= **–**1.6x10 ^{-19} C.**

When a charge *q*** **moving at velocity
**v**
crosses a magnetic field B* *perpendicular to its field
lines, the magnetic field exerts a force F_{m} on the
charge **perpendicular** to the plane of v** **and
B. The magnitude of F

F** _{m
}= **|

The
perpendicularity of
F_{m} and
v
guarantees a centripetal force

that is indeed the magnetic force **F _{m}**

Dividing both sides by v and solving for **
R**, the radius of revolution, results in

If **an electron** of mass M (to be determined),
whose charge is the known value* –*e* ,*
moving at speed v, crosses a magnetic field of strength
B,
it will be given a radius of revolution

( 1 )

The difficult variable to measure in equation
(1) is v,**
**the (magnitude of) the velocity of the electron

P.E. lost = K.E gained.

or

**
eV = ½ **M** **v^{ 2}.

From this equation,
v** ^{ 2}
**may be calculated as

( 2 )

Solving **(1)** for
v and then **squaring** it yields:

( 3 )

Equating (2) and (3), gives:

Dividing both sides by (e/M),

( 4 )

This equation will be used to measure M, the **mass
of an electron**.

__Procedure:__

A **tuning-eye** is an
electronic device widely used in **older non-transistor radios**. It was
used as a visual indicator for best tuning on a desired station. When the tiny
filament in a tuning eye is given a low voltage (V_{1}), it warms up and
glows red, as does an electric heater. In this heated state, the filament
releases electrons. Another voltage (V) may be used to create an
electric field in which the released electrons can be energized, accelerated,
and brought into motion toward a positive dish. The negative filament, the
positive dish, and the two voltage sources are shown below:

The positive dish-like surface is coated with a metal oxide
that glows green/blue as electrons hit it. A metal cap is placed over the
element which is held by three thin legs. These legs cast a shadow on the dish,
making straight dark lines on it when the tuning-eye tube is in use. Increasing
V makes the dish glow brighter. An instruction comes with each
tuning-eye tube that must be followed for proper use. The following steps should
be taken**:**

- Connect the filament wires as indicated in the
instruction to an appropriate voltage V
_{1}. - Wait a few seconds for the filament to warm up and observe its reddish color.
- Connect the other wires as indicated in the instruction to the second appropriate source and increase the voltage to the appropriate level V and observe that the dish attains a bluish or greenish color. Pay attention to the shadow cast on the dish by the cap’s legs and note that they are straight lines as viewed from the top of the tuning eye.
- Connect a pre-selected
**solenoid**(with known number of turns per meter) to an appropriate power supply that can provide a few amperes. An ammeter must be placed in the solenoid circuit for a more-accurate current measurement. Note that the**ammeter**wire must be put in its**10-Amp setting.** - With a current of about
**1A**passing through the solenoid, place the solenoid over the tuning-eye tube so that the filament is positioned at the center of it, and observe how the legs’ shadows (straight lines to begin with) bend as the magnet is lowered. The value you later calculate for**B**, magnetic field strength, actually occurs at the middle of the solenoid; therefore, make sure that the filament is precisely inside and at the center of the solenoid. - Adjust the dish voltage
**cylindrical****non-metallic**object that goes into the solenoid may be used. While holding that object inside the solenoid and looking straight down on to it and the top of the tuning eye, try to match the curvature of the shadow with the curvature of the object by adjusting V and I. - Try
**three**different round objects and obtain three different sets of V, I**,**and R. - For each set, calculate B = μ
_{o}n I , where n is the**number of****turns per meter**of the solenoid. -
## Use B, V, and

**(4).** - Find a
**mean value for**M using the three values calculated. This is the**measured value**.

__Data:__

__Given: __

** **

M_{accepted
}= 9**.**11x10^{-31}
kg.

n** =** number of turns per
meter of the solenoid obtained from the manufacturer’s
paper.

μ_{o} = 4 π
x 10^{-7} (*T m/A*)

__Measured:__

** ** For each set:
V,
I, and R

__Calculations:__

Follow the steps in Procedure.

__
__

__Comparison of the
Results:__

The accepted and measured values of M may be used to obtain a percent error:

__Conclusion:__
To be explained by students

__Discussion:__
To be explained by students