EMG-24

Loop dipole m

Magnetic moment of a current loop.

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GoverningLoop dipole m

Governing equation

m=I A

$I \in \left[0.1, 20\right]$

where

I: I (A)
A: A (cm²)
m: Loop dipole m (A·m²)

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

m=I A

$I \in \left[0.1, 20\right]$

$I = 0.1$ $m = 1.2\times 10^{-4}$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.1,\quad I_{\max} = 20

$I \in \left[0.1, 20\right]$

$I = 0.1$ $I = 0.1$

Along the curve

③

Response curve — green

m=I A

$I \in \left[0.1, 20\right]$

$I = 0.1$ $m = 1.2\times 10^{-4}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}m}{\mathrm{d}I}

$I \in \left[0.1, 20\right]$

$I = 0.225$ $m^{\prime} = 0.001$

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-24 — Loop dipole m) is the form associated with Loop dipole m. Working symbols: $I$ , $A$ $\rightarrow$ $m$ . Magnetic moment of a current loop. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

m

from

I

A

in Electromagnetism via

m=I A

Magnetic moment of a current loop. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I = 2.000\,\mathrm{A}

A = 12.000\,\mathrm{cm^{2}}

, the governing relation

m=I A

yields

m = 0.002\,\mathrm{A·m^{2}}

. 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

I I2 AA A12 cm²

Outputs

Loop dipole m m0.002 A·m²

Reading speed

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Narration of this film

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

Magnetic moment of a current loop. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube