On August 29, 1831, English experimental physicist Michael Faraday (1791–1867) at the Royal Institution in London made one of the most monumental experimental discoveries in scientific history: electromagnetic induction.

Eleven years after Hans Christian Ørsted proved that electric currents generate magnetic fields, Faraday demonstrated the converse: a changing magnetic field generates an electric current in a closed circuit.

Published in his Experimental Researches in Electricity (presented to the Royal Society on November 24, 1831), Faraday’s discovery yielded Faraday’s Law of Induction ($\mathcal{E} = -d\Phi_B / dt$). This single physical law enabled modern electric power generation, inspired Maxwell’s field equations, guided Albert Einstein to Special Relativity, and underpins magnetic flux quantization in superconducting quantum computers.

The Historic 1831 Experiments & Physical Intuition

Faraday performed three seminal series of experiments in the autumn of 1831 that unraveled the mechanisms of electromagnetic induction:

1. The Soft Iron Ring Experiment (August 29, 1831)

Faraday wound two independent coils of insulated copper wire around opposite sides of a soft iron ring ($6\,\text{inches}$ in external diameter). Connecting a voltaic battery to the primary coil caused a brief deflection on a galvanometer attached to the secondary coil.

Crucially, Faraday noticed that current flowed in the secondary coil only at the exact moments when the primary battery was connected or disconnected—establishing that a changing magnetic state, rather than a steady magnetic field, is required to induce electricity.

2. The Moving Bar Magnet Experiment (October 17, 1831)

Faraday plunged a cylindrical permanent steel bar magnet into the center of a hollow wire solenoid connected to a galvanometer:

  • Moving the magnet into the coil induced a transient electric current in one direction.

  • Holding the magnet motionless inside the coil produced zero current.

  • Withdrawing the magnet induced a current in the exact opposite direction.

3. The Faraday Disk / Homopolar Generator (October 28, 1831)

To generate a continuous rather than transient electric current, Faraday mounted a $12\text{-inch}$ copper disk on a brass axle between the magnetic poles of a large permanent horseshoe magnet. Rotating the copper disk produced a continuous direct electric current ($DC$) between the axle and the disk’s outer rim—inventing the world’s first electric generator and dynamo.

Mathematical Formulation: Faraday’s & Lenz’s Laws

James Clerk Maxwell and Heinrich Lenz formalized Faraday’s experimental discovery into the rigorous mathematical language of classical electrodynamics:

1. Magnetic Flux ($\Phi_B$)

The total magnetic flux $\Phi_B$ passing through a surface $S$ bounded by a closed conductive loop is defined as the surface integral of the magnetic field $\mathbf{B}$:

$$\Phi_B = \iint_S \mathbf{B} \cdot d\mathbf{A}$$

Where $d\mathbf{A} = \hat{\mathbf{n}} dA$ is the vector differential area element.

2. Faraday’s Law of Induction & Lenz’s Law

The electromotive force $\mathcal{E}$ induced in a closed circuit loop equals the negative time rate of change of magnetic flux:

$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

Where the negative sign ($\mathbf{-}$) embodies Lenz’s Law (Heinrich Lenz, 1834): the induced electric current flows in a direction such that its own secondary magnetic field opposes the original change in magnetic flux, enforcing energy conservation.

3. Maxwell-Faraday Differential Equation

Expressed in terms of the induced electric field vector $\mathbf{E}$:

$$\oint_C \mathbf{E} \cdot d\boldsymbol{\ell} = -\frac{\partial}{\partial t} \iint_S \mathbf{B} \cdot d\mathbf{A}$$

By Stokes’ Theorem, the differential form of Faraday’s Law becomes the third of Maxwell’s Equations:

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$

This equation proves that a time-varying magnetic field acts as a source of a non-conservative, rotational electric field $\mathbf{E}$.

Faraday’s Induction & Einstein’s Special Relativity (1905)

In the famous opening paragraph of his 1905 Special Relativity paper “Zur Elektrodynamik bewegter Körper”, Albert Einstein highlighted a deep asymmetry in classical electrodynamics regarding Faraday’s induction:

  • If a magnet moves relative to a stationary conductor, a electric field $\mathbf{E} = -\partial\mathbf{B}/\partial t$ is created, producing a current.

  • If the conductor moves relative to a stationary magnet, no electric field is created; instead, the magnetic Lorentz force $\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$ acts on the conductor’s electrons.

Einstein realized that the observable current is identical in both cases. Demanding that the laws of physics be symmetric under relative motion led Einstein to formulate Special Relativity, proving that electric and magnetic fields transform into one another under Lorentz transformations:

$$\mathbf{E}' = \gamma \left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right)$$

Bridge to Quantum Physics & Superconducting Flux Quantization

Faraday’s classical law of induction extends into modern quantum state control:

1. Superconducting Persistent Currents & Zero Resistance

In a closed superconducting ring below its critical temperature ($T < T_c$), an applied magnetic field induces a screening supercurrent via Faraday’s Law. Because superconductors possess zero electrical resistance ($\rho = 0$), these induced supercurrents flow indefinitely without decaying.

2. Quantum Magnetic Fluxoid Quantization

In 1961, Deaver, Fairbank, Doll, and Näbauer experimentally verified that the total magnetic flux $\Phi$ trapped inside a superconducting loop is strictly quantized in integer steps of the magnetic flux quantum $\Phi_0$:

$$\Phi = n \Phi_0 = n \frac{h}{2e} \quad (n = 0, 1, 2, \dots)$$

Where $\Phi_0 = \frac{h}{2e} \approx 2.067837 \times 10^{-15}\,\text{Wb}$ (Weber).

3. Superconducting Quantum Bits (SQUIDs & Transmons)

Superconducting Quantum Interference Devices (SQUIDs) and transmon qubits (powering IBM Quantum Heron and Google Sycamore processors) utilize Josephson junctions embedded in superconducting loops.

These quantum processors tune qubit transition frequencies ($\omega_{01}$) and execute single- and two-qubit quantum logic gates by applying microscopic magnetic flux pulses through the loop—a direct quantum application of Michael Faraday’s 1831 induction discovery.

Key Takeaways

  • Year: 1831

  • Key Figure: Michael Faraday (English Experimentalist & Royal Institution Professor)

  • Core Discovery: Discovered that a changing magnetic flux induces an electromotive force (EMF) and electric current in a closed loop ($\mathcal{E} = -d\Phi_B/dt$).

  • Field Invention: Proved that time-varying magnetic fields create rotational electric fields ($\nabla \times \mathbf{E} = -\partial\mathbf{B}/\partial t$).

  • Relativistic Inspiration: Guided Einstein (1905) to Special Relativity by revealing the physical equivalence of magnet motion and conductor motion.

  • Quantum Relevance: Underpins persistent currents in superconductors, SQUID magnetometers, and magnetic flux quantization ($\Phi_0 = h/2e$) in superconducting quantum processors.