In 1895, Dutch theoretical physicist Hendrik Antoon Lorentz (1853–1928) published his landmark monograph in Leiden titled “Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern”.

Lorentz formulated the complete Lorentz Force Law, defining the net electromagnetic force $\mathbf{F}$ exerted by electric fields $\mathbf{E}$ and magnetic fields $\mathbf{B}$ on a point charge $q$ moving with velocity $\mathbf{v}$.

The Lorentz Force Equation

$$\mathbf{F} = q \left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right)$$

Where:

  • $\mathbf{F}$ is the total electromagnetic force vector ($\text{Newtons}$).
  • $q$ is the electric charge of the subatomic particle ($\text{Coulombs}$).
  • $\mathbf{E}$ is the electric field vector ($\text{Volts/meter}$).
  • $\mathbf{v}$ is particle velocity ($\text{meters/second}$).
  • $\mathbf{B}$ is magnetic flux density ($\text{Tesla}$).

Physical Breakdown

  1. Electric Force ($\mathbf{F}_E = q \mathbf{E}$): Accelerates charged particles parallel to the electric field lines regardless of velocity.
  2. Magnetic Force ($\mathbf{F}_M = q (\mathbf{v} \times \mathbf{B})$): Acts perpendicular to both velocity and magnetic field vectors, deflecting moving charges into helical cyclotron orbits ($\omega_c = q B / m$).

Key Takeaways

  • Year: 1895
  • Key Figure: Hendrik Lorentz (Dutch Theoretical Physicist)
  • Core Discovery: Formulated the Lorentz Force Law ($\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$).
  • Fundamental Law: Governs particle dynamics in mass spectrometers, particle accelerators, and cathode ray tubes.
  • Quantum Relevance: Enters the minimal coupling Hamiltonian ($\hat{H} = \frac{1}{2m}(\hat{\mathbf{p}} - q\mathbf{A})^2 + q\phi$) in quantum mechanics.