ELC-29

Faraday induced EMF

ε = −N ΔΦ/Δt. A changing flux through N turns.

Reading speed

FieldsFaraday 1831

Governing equation

\mathcal{E}=-N\dfrac{\Delta\Phi}{\Delta t}

$\Delta t \in \left[0.2, 200\right]$

where

N: Turns (—)
\Delta\Phi: Flux change (mWb)
\Delta t: Time interval (ms)
\mathcal{E}: Induced EMF (V)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathcal{E}=-N\dfrac{\Delta\Phi}{\Delta t}

$\Delta t \in \left[0.2, 200\right]$

$\Delta t = 0.2$ $\mathcal{E} = -800$

Along the curve

②

Domain of the variable — blue

\Delta t_{\min} = 0.2,\quad \Delta t_{\max} = 200

$\Delta t \in \left[0.2, 200\right]$

$\Delta t = 0.2$ $\Delta t = 0.2$

Along the curve

③

Response curve — green

\mathcal{E}=-N\dfrac{\Delta\Phi}{\Delta t}

$\Delta t \in \left[0.2, 200\right]$

$\Delta t = 0.2$ $\mathcal{E} = -800$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\mathcal{E}}{\mathrm{d}\Delta t}

$\Delta t \in \left[0.2, 200\right]$

$\Delta t = 1.457$ $\mathcal{E}^{\prime} = 294.9$

Along the curve

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-29 — Faraday induced EMF) is the form associated with Faraday 1831. Working symbols: $N$ , $\Delta\Phi$ , $\Delta t$ $\rightarrow$ $\mathcal{E}$ . Faraday: the induced electric field around a loop equals minus the rate of flux through it. Lenz gives the sign.

Purpose

Purpose: compute

\mathcal{E}

from

N

\Delta\Phi

\Delta t

in Electrical via

\mathcal{E}=-N\dfrac{\Delta\Phi}{\Delta t}

ε = −N ΔΦ/Δt. A changing flux through N turns. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

N = 80.000\,\mathrm{—}

\Delta\Phi = 2.000\,\mathrm{mWb}

\Delta t = 8.000\,\mathrm{ms}

, the governing relation

\mathcal{E}=-N\dfrac{\Delta\Phi}{\Delta t}

yields

\mathcal{E} = -20.000\,\mathrm{V}

. A coil, a plunging magnet, a voltmeter kick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Turns N80 —Flux change \Delta\Phi2 mWbTime interval \Delta t8 ms

Outputs

Induced EMF \mathcal{E}-20.000 V

Reading speed

Watch on YouTube

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Narration of this film

A coil, a plunging magnet, a voltmeter kick.

Faraday: the induced electric field around a loop equals minus the rate of flux through it. Lenz gives the sign.

Reading speed

Watch on YouTube