The objective of this experiment is to measure the mass of electron by using electric and magnetic fields.
A tuning-eye, a high-voltage dc source, two 12V 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), connecting wires, and a calculator
A set of perpendicular electric and magnetic fields may be used to measure the electron mass taking the electron charge e = -1.6x10-19C as a known value.
When charge q moving at speed v crosses magnetic field B perpendicular to its field lines, the magnetic field exerts force Fm on the charge perpendicular to the plane of v and B. The magnitude of Fm is given by
Fm = |qvB|.
The perpendicularity of Fm and v guarantees a centripetal force
that is indeed the magnetic force Fm itself. The centripetal force Fc forces the electron to travel in a circular path. Equating Fm and Fc , yields:
Dividing both sides by v and solving for R, the radius of rotation, results in
If an electron of mass M (to be determined), with the known charge e moving at speed v crosses a magnetic field of strength B, it will be given a radius of revolution R that can be calculated from the equation:
The difficult variable to measure in equation (1) is v, the electron speed. Speed v can be determined as described below. In the experiment, we arrange for electrons to gain speed v in an electric field of voltage V.
P.E. loss = K.E gain
eV = 0.5Mv 2.
From this equation, v2 may be calculated as
Solving (1) for v and then squaring it yields:
Equating (2) and (3), gives:
Dividing both sides by e/M,
This equation in which V is the voltage of the high-voltage source will be used to solve for M, the electron mass.
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 V1, it warms up and glows red like 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 shadow on the dish, making straight lines on it when the tuning-eye is in use. Increasing V makes the dish glow brighter. An instruction comes with each tuning-eye that must be followed for proper use. The following steps should be taken:
Given: Maccptd = 9.11x10 -31 kg.
n = number of loops per meter of the solenoid from its specifications.
μo = 4π x10 -7Tm/A.
Measured: V, I, and R for each trial (round object)
Follow the steps under "Procedure."
Comparison of the Results:
The accepted and measured values of M may be used to obtain a % error.
Conclusion: To be explained by students.
Discussion: To be explained by students.