EMG-32

Magnetic energy density

Linear-media magnetic energy.

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GoverningMagnetic energy density

Governing equation

u=B^2/(2\\mu_0)

$B \in \left[0.01, 2\right]$

where

B: B (T)
u: Magnetic energy density (J/m³)

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

u=B^2/(2\\mu_0)

$B \in \left[0.01, 2\right]$

$B = 0.01$ $u = 39.79$

Along the curve

②

Domain of the variable — blue

B_{\min} = 0.01,\quad B_{\max} = 2

$B \in \left[0.01, 2\right]$

$B = 0.01$ $B = 0.01$

Along the curve

③

Response curve — green

u=B^2/(2\\mu_0)

$B \in \left[0.01, 2\right]$

$B = 0.01$ $u = 39.79$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}u}{\mathrm{d}B}

$B \in \left[0.01, 2\right]$

$B = 0.023$ $u^{\prime} = 17918$

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-32 — Magnetic energy density) is the form associated with Magnetic energy density. Working symbols: $B$ $\rightarrow$ $u$ . Linear-media magnetic energy. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

u

from

B

in Electromagnetism via

u=B^2/(2\\mu_0)

Linear-media magnetic energy. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

B = 0.200\,\mathrm{T}

, the governing relation

u=B^2/(2\\mu_0)

yields

u = 15915.964\,\mathrm{J/m^{3}}

. 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

B B0.2 T

Outputs

Magnetic energy density u15915.964 J/m³

Reading speed

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Narration of this film

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

Linear-media magnetic energy. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube