EMG-03

Biot–Savart infinite wire

B = μ0 I /(2π r) around a long straight wire.

Reading speed

MagnetostaticsBiot–Savart 1820

Governing equation

B=\dfrac{\mu_0 I}{2\pi r}

where

I: Current (A)
r: Radial distance (cm)
B: Magnetic field (µT)

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-03 — Biot–Savart infinite wire) is the form associated with Biot–Savart 1820. Working symbols: $I$ , $r$ $\rightarrow$ $B$ . Integrating the Biot–Savart kernel μ0 I dl×r̂ /(4π r²) along an infinite line yields Ampère's concentric field.

Purpose

Purpose: compute

B

from

I

r

in Electromagnetism via

B=\dfrac{\mu_0 I}{2\pi r}

B = μ0 I /(2π r) around a long straight wire. 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 = 10.000\,\mathrm{A}

r = 5.000\,\mathrm{cm}

, the governing relation

B=\dfrac{\mu_0 I}{2\pi r}

yields

B = 40.000\,\mathrm{\mu T}

. Infinite straight wire in vacuum. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Current I10 ARadial distance r5 cm

Outputs

Magnetic field B40.000 µT

Reading speed

Watch on YouTube

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Narration of this film

Infinite straight wire in vacuum.

Integrating the Biot–Savart kernel μ0 I dl×r̂ /(4π r²) along an infinite line yields Ampère's concentric field.

Reading speed

Watch on YouTube