Cathode Ray Tube and Thomson's Electron Charge-to-Mass Determination

A glass tube from which most of the air has been evacuated (evacuated environment to allow a free beam).
Two metal plates are connected to a high voltage source; the negatively charged plate is the cathode and emits the cathode ray.
The positively charged plate is the anode; the cathode ray is attracted to the anode and passes through a small hole to travel toward the other end of the tube.
When the ray strikes a specially coated surface along the tube, it produces strong fluorescence (visual display of the beam).
Path of the beam: from the cathode to the anode, through a hole, and onward to the far end of the tube.
The setup demonstrates how a beam of charged particles can be steered and visualized inside an evacuated glass envelope.

When an electric field is applied across the tube, the cathode ray is attracted to the positively charged plate, indicating the particles are negatively charged.
The particles observed are electrons.
A moving charged body behaves like a tiny magnet and interacts with an external magnetic field; the electrons in the ray are deflected by a magnetic field.
Reversing the direction of the external magnetic field causes the beam to deflect in the opposite direction, confirming the charge sign and magnetic interaction.

The beam can be deflected by both electric and magnetic fields, showing that moving charges respond to electromagnetic forces.
The deflection provides a method to study properties of the particles (charge, mass) via the forces acting on them.
The observed deflection behavior under field reversal supports the conclusion that cathode rays are negatively charged particles (electrons).

J. J. Thomson determined the charge-to-mass ratio,
by adjusting the electric field so that the electrostatic deflection angle $ hetae$ matched the magnetic deflection angle $ hetab$ (i.e., the two deflections were made to cancel or balance against each other for a measurable condition).
In Thomson’s setup:
- $e$ = applied electric field (electric field strength)
- $ heta$ = deflection angle (with subscripts $e$ for electrostatic and $b$ for magnetic)
- $b$ = applied magnetic field
- $l$ = distance traveled by the cathode rays
The balance condition is described as the electrostatic deflection being the same as the magnetic deflection, which allowed the calculation of the charge-to-mass ratio of the electron.
Result: the charge-to-mass ratio of the electron is $\frac{e}{m_e} = -1.76 \times 10^{8}\ \text{C g}^{-1}$
- sign indicates a negative charge.
In SI units, this equivalent value is $\frac{e}{m_e} = -1.76 \times 10^{11}\ \text{C kg}^{-1}.$
The negative sign reflects the electron’s negative charge.
Note: The transcript mentions the equation used to relate $e$, $ hetae$, $b$, $ hetab$, and $l$ but does not display the explicit form of the equation.

Provides the first quantitative measurement of the electron’s charge-to-mass ratio, a foundational result in atomic and particle physics.
Confirms that cathode rays are electrons (negatively charged constituents of atoms).
Demonstrates a practical method for probing fundamental particle properties using just electric and magnetic fields.
Establishes key experimental techniques that underpin later instrumentation in physics (e.g., mass-to-charge measurements, particle beam experiments).
The discovery and characterization of the electron contribute to the development of atomic theory and the understanding of electrical charge as a fundamental property.

The cathode ray tube described is a precursor to the television tube and other CRT devices.
The fluorescence screen provides a visible indication of beam position and behavior, illustrating how electron beams can produce images and signals.
The dual-field deflection method (electric and magnetic) laid groundwork for technologies that steer charged particles in accelerators, oscilloscopes, and display equipment.

Lorentz force concept: moving charges experience force due to electric and magnetic fields, $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, which explains deflection in both fields.
The experiment connects macroscopic measurements (deflection angles) to microscopic properties (charge-to-mass ratio) of fundamental particles.
Demonstrates the particle nature of electrical phenomena and supports the idea that atoms contain subatomic components (electrons).

The transcript notes the presence of an equation used to link $e$, $\thetae$, $b$, $\thetab$, and $l$, but the explicit form is not shown in the text provided.
The reported value for $\dfrac{e}{m_e}$ aligns with historical measurements that established the electron as a fundamental, negatively charged particle.
Practical implications include improved measurement techniques for particle properties and the eventual development of devices relying on controlled electron beams.

Balance condition in Thomson’s experiment: $\theta<em>e = \theta</em>b$
Electron charge-to-mass ratio (transcript value): $\frac{e}{m_e} = -1.76 \times 10^{8}\ \text{C}\ \text{g}^{-1}$
In SI units: $\frac{e}{m_e} = -1.76 \times 10^{11}\ \text{C}\ \text{kg}^{-1}$
Conceptual variables used:
- $e$: applied electric field (electric field strength)
- $\theta_e$: electrostatic deflection angle
- $\theta_b$: magnetic deflection angle
- $b$: applied magnetic field
- $l$: distance traveled by the cathode rays