EMG-09

Long-solenoid field

B = μ0 n I inside an infinite solenoid.

Reading speed

MagnetostaticsAmpère

Governing equation

B=\mu_0 n I,\quad n=N/L

$I \in \left[0.05, 50\right]$

where

n: Turn density (1/m)
I: Current (A)
B: Interior field (mT)

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

B=\mu_0 n I,\quad n=N/L

$I \in \left[0.05, 50\right]$

$I = 0.05$ $B = 0.126$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.05,\quad I_{\max} = 50

$I \in \left[0.05, 50\right]$

$I = 0.05$ $I = 0.05$

Along the curve

③

Response curve — green

B=\mu_0 n I,\quad n=N/L

$I \in \left[0.05, 50\right]$

$I = 0.05$ $B = 0.126$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}B}{\mathrm{d}I}

$I \in \left[0.05, 50\right]$

$I = 0.364$ $B^{\prime} = 2.513$

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-09 — Long-solenoid field) is the form associated with Ampère. Working symbols: $n$ , $I$ $\rightarrow$ $B$ . Ampère's law on a rectangular loop with one side inside a tightly wound infinite solenoid gives B = μ0 n I and B = 0 outside.

Purpose

Purpose: compute

B

from

n

I

in Electromagnetism via

B=\mu_0 n I,\quad n=N/L

B = μ0 n I inside an infinite solenoid. 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 = 2000.000\,\mathrm{1/m}

I = 3.000\,\mathrm{A}

, the governing relation

B=\mu_0 n I,\quad n=N/L

yields

B = 7.540\,\mathrm{mT}

. Infinite, tightly wound, vacuum core. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Turn density n2000 1/mCurrent I3 A

Outputs

Interior field B7.540 mT

Reading speed

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Narration of this film

Infinite, tightly wound, vacuum core.

Ampère's law on a rectangular loop with one side inside a tightly wound infinite solenoid gives B = μ0 n I and B = 0 outside.

Reading speed

Watch on YouTube