ELC-30

Ampère solenoid field

B = μ0 n I inside a long solenoid, n = N/ℓ.

Reading speed

MagneticsAmpère

Governing equation

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

$I \in \left[0.05, 40\right]$

where

N: Turns (—)
\ell: Length (cm)
I: Current (A)
B: Interior B (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.

00:0 / 00:08

①

Governing law — red

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

$I \in \left[0.05, 40\right]$

$I = 0.05$ $B = 0.126$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.05,\quad I_{\max} = 40

$I \in \left[0.05, 40\right]$

$I = 0.05$ $I = 0.05$

Along the curve

③

Response curve — green

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

$I \in \left[0.05, 40\right]$

$I = 0.05$ $B = 0.126$

Along the curve

④

Rate of change — amber

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

$I \in \left[0.05, 40\right]$

$I = 0.301$ $B^{\prime} = 2.513$

Along the curve

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-30 — Ampère solenoid field) is the form associated with Ampère. Working symbols: $N$ , $\ell$ , $I$ $\rightarrow$ $B$ . Ampère's law on a rectangle that runs inside the solenoid: ∮ B·dl = μ0 N I, so B = μ0 (N/ℓ) I.

Purpose

Purpose: compute

B

from

N

\ell

I

in Electrical via

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

B = μ0 n I inside a long solenoid, n = N/ℓ. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

N = 400.000\,\mathrm{—}

\ell = 20.000\,\mathrm{cm}

I = 2.000\,\mathrm{A}

, the governing relation

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

yields

B = 5.027\,\mathrm{mT}

. A solenoid, an interior B arrow, a turn density. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Turns N400 —Length \ell20 cmCurrent I2 A

Outputs

Interior B B5.027 mT

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A solenoid, an interior B arrow, a turn density.

Ampère's law on a rectangle that runs inside the solenoid: ∮ B·dl = μ0 N I, so B = μ0 (N/ℓ) I.

Reading speed

Watch on YouTube