The Lorentz Force

History

     Early attempts to describe electromagnetic force can be dated back to the 18th century, with Johann Tobias Mayer (1760) and Henry Cavendish (1762) suggesting that the force on magnetic poles and electrically charged objects obeyed an inverse-square law. There was a lack of experimental evidence until Charles-Augustin de Coulomb (1784) used a torsion balance to show that this was the case. Andre-Marie Ampere (1820) was the one who created the formula for angular dependence of the force between two current elements. Michael Faraday is the man responsible for the modern concept of electric and magnetic fields, which was later given mathematical description by Lord Kelvin and James Clerk Maxwell (1865).

     Sir Joseph John Thomson was first in attempting the derivation of the electromagnetic forces on a moving charged particle from Maxwell's equations (1881). In the paper he published, he gave the force as:

Thomson had the correct form of the equation, but due to some miscalculations and an incomplete description of the displacement current, included an incorrect scale of one-half at the front of the formula. Oliver Heaviside, who is responsible for the modern vector notation and also applied it to Maxwell's equations, fixed Thomson's mistakes and derived the correct form of the formula. For the modern formulation, Hendrik Lorentz (1892) arrived at the modern form which takes into account the total force from both the electric and magnetic fields.