The experiment is a chain that turns a visible beam deflection into \(|q|/m\). First, the Lorentz force \(\vec F=q(\vec E+\vec v\times\vec B)\) is used in capacitor A: the electric and magnetic forces cancel only for particles with \(v_x=E_{yA}/B_z\). This is a velocity selector.
Then the selected beam enters capacitor B, where the electric field bends the trajectory. Measuring the total displacement \(d\), together with the known geometry \(l\) and \(L\), gives \(|q|/m=2dv_x^2/[E_{yB}l(l+2L)]\). The conceptual conclusion comes after the algebra: the ratio is so large that the beam particles must be very light compared with Hydrogen ions, pointing to the electron.
The cathode-ray tube turns a qualitative observation into a measurement. The beam is accelerated, velocity-selected and then deflected. Each stage removes one unknown until the charge-to-mass ratio can be inferred.
In the selector region, the electric and magnetic forces point in opposite directions. A particle goes straight only when their magnitudes cancel:
Only particles with this selected speed pass through the collimator, so the later deflection can be interpreted without also solving for \(v_x\).
In the second capacitor, the electric field gives a vertical acceleration \(a_y=|q|E_{yB}/m\). The observed displacement depends on this acceleration and on the time the beam spends in and after the plates.
The ratio is much larger than the corresponding value for Hydrogen ions. Thomson interpreted this as evidence for a much smaller mass carrier: the electron.
The atom is no longer indivisible. Cathode rays introduce a charged microscopic constituent and force atomic models to include internal structure. This is a prerequisite for Bohr's later atomic model, where the electron becomes the moving charge whose allowed states must be explained.
This page is designed to support short guided exercises on: Thomson's charge-to-mass measurement, atomic divisibility and the first subatomic particle picture.
- Use from this page: the definitions, physical setup, highlighted equations and conceptual links needed to start a first calculation or explanation.
- Keep in the book: complete derivations, extended historical discussion, worked solutions and the full textbook narrative remain in the original chapter and linked book resources.
- Good exercise balance: ask the student to identify assumptions, apply one relation, and interpret the result physically, without requiring material not introduced on this page.
Use these anchors to design compact exercises. The exercise should be answerable from this page plus standard algebra, while longer derivations, full worked examples and broader context should point back to the original book.
- Focus: Thomson's charge-to-mass measurement, atomic divisibility and the first subatomic particle picture.
- Conceptual check: state what the main result says physically before using it algebraically.
- Equation: \[\vec F=q(\vec E+\vec v\times \vec B)\]
- Equation: \[|q|E_{yA}=|q|v_xB_z.\]
- Equation: \[v_x=\frac{E_{yA}}{B_z}\]
- Boundary: use this page for setup and first-step reasoning; cite the book for longer derivations, complete experimental history or solved-problem detail.
- Typical task: derive, interpret, or apply the relation above to a simple case without introducing topics outside this page.