EMG-29

Faraday loop

Induced emf.

Reading speed

GoverningFaraday loop

Governing equation

\\mathcal{E}=-d\\Phi/dt

$dt \in \left[0.001, 1\right]$

where

dPhi: dPhi (Wb)
dt: dt (s)
emf: Faraday loop (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}=-d\\Phi/dt

$dt \in \left[0.001, 1\right]$

$dt = 0.001$ $emf = -20$

Along the curve

②

Domain of the variable — blue

dt_{\min} = 0.001,\quad dt_{\max} = 1

$dt \in \left[0.001, 1\right]$

$dt = 0.001$ $dt = 0.001$

Along the curve

③

Response curve — green

\\mathcal{E}=-d\\Phi/dt

$dt \in \left[0.001, 1\right]$

$dt = 0.001$ $emf = -20$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}emf}{\mathrm{d}dt}

$dt \in \left[0.001, 1\right]$

$dt = 0.007$ $emf^{\prime} = 1474.3$

Along the curve

Lecture brief

Historical brief

Coulomb, Gauss, Ampère, Faraday and Maxwell (1861–65) unified charge, current and light. The lab computes fields, induction, Poynting flux and the electromagnetic wave in SI. This sheet (EMG-29 — Faraday loop) is the form associated with Faraday loop. Working symbols: $dPhi$ , $dt$ $\rightarrow$ $emf$ . Induced emf. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

emf

from

dPhi

dt

in Electromagnetism via

\\mathcal{E}=-d\\Phi/dt

Induced emf. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

dPhi = 0.020\,\mathrm{Wb}

dt = 0.050\,\mathrm{s}

, the governing relation

\\mathcal{E}=-d\\Phi/dt

yields

emf = -0.400\,\mathrm{V}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

dPhi dPhi0.02 Wbdt dt0.05 s

Outputs

Faraday loop emf-0.400 V

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Induced emf. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube