ELC-28

Wire field B=μI/2πr

B = μ I /(2π r) around a long straight wire.

Reading speed

MagneticsBiot–Savart

Governing equation

B=\dfrac{\mu I}{2\pi r}

where

I: Current (A)
r: Radius (mm)
\mu_r: Relative μ (—)
B: Flux density (µT)

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-28 — Wire field B=μI/2πr) is the form associated with Biot–Savart. Working symbols: $I$ , $r$ , $\mu_r$ $\rightarrow$ $B$ . Ampère's law ∮ B·dl = μ I on a circle of radius r, or Biot–Savart integrated along the line.

Purpose

Purpose: compute

B

from

I

r

\mu_r

in Electrical via

B=\dfrac{\mu I}{2\pi r}

B = μ I /(2π r) around a long straight wire. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I = 20.000\,\mathrm{A}

r = 25.000\,\mathrm{mm}

\mu_r = 1.000\,\mathrm{—}

, the governing relation

B=\dfrac{\mu I}{2\pi r}

yields

B = 160.000\,\mathrm{\mu T}

. A wire, concentric B circles, a radius r. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Current I20 ARadius r25 mmRelative μ \mu_r1 —

Outputs

Flux density B160.000 µT

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A wire, concentric B circles, a radius r.

Ampère's law ∮ B·dl = μ I on a circle of radius r, or Biot–Savart integrated along the line.

Reading speed

Watch on YouTube