Microphones

Every time you speak into a microphone at a school event or record a voice message on your phone, electromagnetic induction is silently doing the work. A moving-coil (dynamic) microphone converts the mechanical energy of sound waves — tiny fluctuations in air pressure — into a corresponding electrical signal. The fundamental physics is the same Faraday induction you study in class: a conductor moving through a magnetic field generates an EMF. Sound is a longitudinal pressure wave. When a sound wave strikes the thin plastic diaphragm of a microphone, the diaphragm vibrates back and forth at the same frequency as the sound. Attached to the diaphragm is a small coil of wire (the voice coil) positioned inside the gap of a permanent magnet. As the diaphragm and coil oscillate, the coil cuts through magnetic field lines, and by Faraday's law an alternating EMF is induced — a voltage signal that is an electrical analogue of the original sound wave. Moving-coil microphones are robust, require no external power supply, and produce high-quality audio, which is why they dominate live performance and broadcasting. Understanding how they work ties together several key ideas: the motional EMF of a conductor in a field, Lenz's law (which determines the polarity of the output), and the idea that the amplitude and frequency of the induced EMF mirror the amplitude and frequency of the original sound.

Key takeaways
  • Sound Wave Arrives at the Diaphragm
  • Voice Coil Moves Inside the Magnetic Gap
  • Motional EMF is Induced
  • Alternating Output Mirrors the Sound
  • Lenz's Law and Signal Polarity

Sound Wave Arrives at the Diaphragm

A sound wave is a series of compressions and rarefactions travelling through air. When it reaches the diaphragm — a lightweight membrane typically 25–50 mm in diameter — the pressure differences exert a net force that pushes and pulls the diaphragm inward and outward at the same frequency as the sound (e.g., 440 Hz for the musical note A4).

Voice Coil Moves Inside the Magnetic Gap

The voice coil is a small cylindrical coil glued to the back of the diaphragm. It sits in a narrow annular gap in a permanent magnet (a ring magnet or pot magnet), so the magnetic field B in the gap points radially — always perpendicular to the axis of the coil. When the diaphragm moves axially (in-and-out), every straight wire segment of the coil moves with velocity v perpendicular to B. This is the classic motional-EMF geometry.

Motional EMF is Induced

For each small segment of wire of length dl moving at velocity v in field B, the force on the free electrons is F = qv × B, displacing charge and generating an EMF. For a coil of N turns, each of circumference C (so effective straight-wire length per turn = C in the radial field), the total motional EMF is ε = NBCv = NB(2πr)v, where r is the coil radius. Since v = dx/dt (the diaphragm velocity), the output voltage is directly proportional to how fast the diaphragm is moving, not its displacement. This means a microphone is a velocity transducer.

Alternating Output Mirrors the Sound

Because the diaphragm oscillates sinusoidally for a pure tone, its velocity also varies sinusoidally: v(t) = Aω cos(ωt) if displacement x(t) = A sin(ωt). The induced EMF is therefore ε(t) = NBCω A cos(ωt) — an AC voltage at the same frequency ω as the sound, with amplitude proportional to both the acoustic amplitude A and the angular frequency ω. For complex sounds (speech, music), the output is a superposition of many such AC components, faithfully reproducing the waveform.

Lenz's Law and Signal Polarity

Lenz's law guarantees that the induced current opposes the motion causing it. When the diaphragm is pushed inward (toward the magnet), the induced current flows in one direction; when pulled outward, it reverses. This opposition slightly damps the motion (the coil acts as a generator with internal resistance), which actually helps control resonance and broadens the frequency response of the microphone.

The Key Equation

ε=NBℓ v\varepsilon = N B \ell \, v
  • \varepsilon — Induced EMF (V (volts)): The instantaneous output voltage of the microphone; it varies in time exactly as the coil velocity varies.
  • N — Number of turns (dimensionless): Total number of wire turns in the voice coil; more turns give larger output for the same motion.
  • B — Magnetic flux density (T (tesla)): Strength of the radial magnetic field in the gap of the permanent magnet; typical values 0.5–1.5 T for microphone magnets.
  • \ell — Effective conductor length (m (metres)): Total length of wire cutting through the field, equal to N × 2πr where r is the coil radius.
  • v — Coil velocity (m s⁻¹): Instantaneous speed of the voice coil (and diaphragm) along the axis; equals dA·ω·cos(ωt) for sinusoidal motion of amplitude A.

Worked Example

Problem. A moving-coil microphone has a voice coil with 80 turns, a coil radius of 4.0 mm, and operates in a magnetic field of 1.2 T. A musician plays a 500 Hz sine tone causing the diaphragm to oscillate with an amplitude of 0.10 mm. (a) What is the maximum velocity of the diaphragm? (b) What is the peak EMF produced by the microphone?

vmax⁡=Aω≈0.314 m s−1,εmax⁡=NB(2πr)vmax⁡≈0.76 Vv_{\max} = A\omega \approx 0.314 \text{ m s}^{-1}, \quad \varepsilon_{\max} = NB(2\pi r)v_{\max} \approx 0.76 \text{ V}

Answer. Peak diaphragm velocity ≈ 0.314 m/s; peak induced EMF ≈ 0.76 V.

Figure
Diagram
Moving-Coil Microphone — Cross-SectionPermanent MagnetN poleGapGap BBCoilDiaphragmv (coil motion)Output: AC voltage ε(t)Soundwaves
Origins · 1 minErnst Werner von Siemens and how this was discovered
EW
Ernst Werner von Siemens
1816–1892 · German

Siemens invented the moving-coil transducer principle in 1874 when he described a 'dynamic' electromechanical device in which a cylindrical coil moved axially in a magnetic gap — the exact geometry used in every moving-coil microphone and loudspeaker today. His patent laid the physical foundation that later engineers, including Rice and Kellogg (who built the first practical moving-coil loudspeaker in 1925), would develop into modern audio technology. Siemens also invented the telegraph pointer, laid the first transatlantic telegraph cable, and founded the company that bears his name — still one of the world's largest engineering firms. The SI unit of electrical conductance, the siemens (S), is named in his honour.

  • Faraday's Law of Electromagnetic Induction — Faraday's law is the fundamental principle behind microphone operation: the rate of change of magnetic flux through the voice coil determines the induced EMF at every instant.
  • Motional EMF — The microphone is a direct application of motional EMF — the formula ε = NBℓv describes exactly how the moving coil generates voltage in the magnetic field gap.
  • Lenz's Law — Lenz's law determines the polarity of the output signal and the electromagnetic damping of the diaphragm, which shapes the microphone's frequency response.
  • Sound Waves and Pressure — Understanding pressure oscillations in sound waves explains what physical input is driving the diaphragm of the microphone.
  • Loudspeakers — A moving-coil loudspeaker is the exact reverse of a microphone: it converts an electrical AC signal into diaphragm motion and sound — the same coil-in-gap geometry operating in reverse.