On October 28, 1879, 24-year-old American graduate student Edwin Herbert Hall (1855–1938), working under Henry Augustus Rowland at Johns Hopkins University, discovered the Hall Effect.

Hall published his discovery in the American Journal of Mathematics (Vol. 2, 1879), proving that when a perpendicular magnetic field is applied to a current-carrying conductor, a transverse electric voltage (Hall Voltage, $V_{\text{H}}$) is generated across the conductor.

Physical Mechanism & Lorentz Force Derivation

Hall placed a thin gold leaf strip carrying electric current $I_x$ between the poles of a powerful electromagnet ($B_z$):

1. Transverse Lorentz Force

Moving charge carriers (charge $q$, drift velocity $v_x$) experience a transverse magnetic Lorentz force along the $y$-axis:

$$\mathbf{F}_y = q (\mathbf{v}_x \times \mathbf{B}_z)$$

2. Hall Electric Field & Voltage Formula

Charge carriers accumulate on one edge of the conductor until the resulting transverse electric field $E_y$ balances the magnetic force ($q E_y = q v_x B_z$):

$$V_{\text{H}} = E_y \cdot w = \frac{I_x B_z}{n q d}$$

Where:

  • $w$ is conductor width, $d$ is thickness.
  • $n$ is charge carrier concentration ($\text{m}^{-3}$).
  • $R_{\text{H}} = 1 / (n q)$ is the material Hall Coefficient.

Sign of Charge Carriers & Quantum Hall Effect

  • Sign of Charge Carriers: The Hall Effect provided the first experimental proof that electric current in metals is carried by negatively charged particles (electrons, $q = -e$) 18 years before J.J. Thomson’s discovery of the electron.
  • Quantum Hall Effect (1980): In 2D electron gases at millikelvin temperatures and high magnetic fields, Klaus von Klitzing discovered that Hall resistance becomes quantized in exact integer steps of the fundamental quantum resistance constant:

$$R_{\text{H}} = \frac{h}{i e^2} \approx \frac{25,812.807\,\Omega}{i} \quad (i = 1, 2, 3, \dots)$$

Key Takeaways

  • Year: 1879
  • Key Figure: Edwin Hall (American Physicist)
  • Core Discovery: Discovered the Hall Effect ($V_{\text{H}} = I B / n q d$), proving electric currents carry negative charge.
  • Diagnostic Tool: Primary technique for measuring semiconductor carrier density ($n$) and mobility ($\mu$).
  • Quantum Relevance: Direct classical precursor to the Nobel Prize-winning Integer and Fractional Quantum Hall Effects.