EMG-14

Faraday induction

ε = − dΦB / dt. A changing flux makes an emf.

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ElectrostaticsFaraday

Governing equation

\mathcal{E}=-N\dfrac{d\Phi_B}{dt}

where

N: Turns (—)
d\Phi_B/dt: Flux rate (Wb/s)
\mathcal{E}: Induced emf (V)

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-14 — Faraday induction) is the form associated with Faraday. Working symbols: $N$ , $d\Phi_B/dt$ $\rightarrow$ $\mathcal{E}$ . Lenz: the induced current fights the change. For a loop, ΦB = B A cosθ.

Purpose

Purpose: compute

\mathcal{E}

from

N

d\Phi_B/dt

in Electromagnetism via

\mathcal{E}=-N\dfrac{d\Phi_B}{dt}

ε = − dΦB / dt. A changing flux makes an 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

N = 50.000\,\mathrm{—}

d\Phi_B/dt = 0.020\,\mathrm{Wb/s}

, the governing relation

\mathcal{E}=-N\dfrac{d\Phi_B}{dt}

yields

\mathcal{E} = -1.000\,\mathrm{V}

. A loop, a plunging magnet, a bouncing needle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Turns N50 —Flux rate d\Phi_B/dt0.02 Wb/s

Outputs

Induced emf \mathcal{E}-1.000 V

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Narration of this film

A loop, a plunging magnet, a bouncing needle.

Lenz: the induced current fights the change. For a loop, ΦB = B A cosθ.

Reading speed

Watch on YouTube