How physics got its right hand: The origins of chiral conventions in electromagnetism

TL;DR

This paper investigates the origins of the standard right-handed conventions in electromagnetism, notably why counterclockwise rotation is defined as positive and how magnetic polarity is established, by tracing historical developments from polar coordinates to Maxwell's consolidation via the London Mathematical Society in 1871. Using historical sources and concrete examples such as Faraday's law $\mathcal{E}=-\frac{d}{dt}\iint_\Sigma \mathbf{B}\cdot d\mathbf{A}$, it shows how choices about coordinate orientation, charge sign, and magnetism polarity would alter sign conventions across Maxwell's equations. It documents the sequence from Newton's early polar-coordinate usage, Franklin's charge definition, Faraday's and Ampère's insights on magnetism, to Maxwell's push for a unified vector-analytic framework, culminating in the LMS decision and Maxwell's subsequent standardization of conventions. The work emphasizes the pedagogical and communicative implications of conventions in physics, illustrating how definitions shape learning, collaboration, and scientific progress.

Abstract

Why do physicists almost universally take the direction of positive rotation to be counterclockwise, and three-dimensional coordinates to be right-handed? This paper traces the historical development of these chiral conventions, with an emphasis on the physical quantity whose direction became the focal point of this discussion in the mid-1800s, the magnetic field. Though these standards are often reduced to mere mathematical, inconsequential choices, an analysis of the impact of Newton, Maxwell, the London Mathematical Society, and others toward the subject can enhance classroom discussion, not only as a contextual sidebar, but also by emphasizing the influence conventions in physics can have on pedagogy, communication, and scientific advancement.

Figures (4)

• Figure 1: Figure from the section "Seventh Manner: For Spirals" from Newton's handwritten draft of Method of Fluxions, which provides one of the earliest uses of polar-type coordinates. To find the tangent DT of the dashed spiral ADE at point D, Newton chooses the $x$ coordinate to be the counterclockwise circumferential length BG and the $y$ coordinate to be the radial length AD. (Cambridge University Library, MS Add. 3960, p. 3:25)
• Figure 2: Faraday's sketches from his 1831 experiments. (Top) If the spiral of wire shown is pushed into the page toward the marked (north) pole of the magnet, a current of electricity $\mathcal{E}$ will be induced in the direction shown. The small arrows intersecting the spiral, which point out from the marked pole, indicate one of Faraday's earliest attempts to visualize "magnetic curves."Faraday1831 (Bottom) Elsewhere, he depicted these curves without a sense of directionality, showing only which end of the magnet was marked or unmarked.Romo1994
• Figure 3: Ampère's little man lies on his back along a partially-drawn equator, with a geographic north-south meridian crossing him left-to-right. An electrical current running along the equator from his feet to his head will produce a magnetic field, which will cause a north-pointing compass placed above him to follow the direction of his left arm.Ampere
• Figure 4: Coordinate systems (cast in modern form; see explanation in text) used by Newton in each of his nine manners from Problem IV ("To draw Tangents to Curves") of Method of Fluxions. They are labeled in the work as follows: (a) First Manner. (b) Second Manner. (c) Third Manner. (d) Fourth Manner. (e) Fifth Manner. (f) Sixth Manner. (g) Seventh Manner: For Spirals. (h) Eighth Manner: For Quadratrices. (i) Ninth Manner.