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Electromagnetism

Magnetic Field Around a Long Straight Wire

A long straight current-carrying wire produces a magnetic field whose magnitude decreases inversely with perpendicular distance.

B = \frac{μ _{0} I}{2 π r}

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Basic algebra, consistent units, and the stated model assumptions

Review statusNeeds review

Source

OpenStax, College Physics 2e, §22.9 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Definition

Understanding the core concept

A long straight current-carrying wire produces a magnetic field whose magnitude decreases inversely with perpendicular distance. Its direction circles the wire according to the right-hand rule.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$B$	Magnetic Field	$T$
$μ_{0}$	Permeability of Free Space	$T \cdot m/A$
$I$	Electric current	$A$
$r$	Perpendicular distance from the wire axis	$m$

Real-World Applications

Where this formula is used in practice

Wire fields

Estimate magnetic field outside a long straight wire.

Current changes

Compare field magnitudes for different currents.

Worked Example

Step-by-step calculation with real numbers

Problem

Find the field magnitude 0.0500 m from a long straight wire carrying 10.0 A.

Given

μ_{0} = 0.00000125663706 T \cdot m/A

I = 10 A

r = 0.05 m

Solution

B = \frac{μ _{0} I}{2 π r}

B = \frac{( 0.00000125663706 T \cdot m/A ) \cdot ( 10 A )}{( 2 \cdot π \cdot ( 0.05 m ) )}

B \approx 0.00004 T

Final Answer

B \approx 0.00004 T

Formula Guide

Info

DifficultyIntermediate

Read Time5 min

PrerequisitesBasic algebra, consistent units, and the stated model assumptions

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, College Physics 2e, §22.9 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.

Assumptions

• Treat the wire as effectively infinitely long and the observation point as outside it.
• Use a steady current in vacuum or a medium with approximately vacuum permeability.

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Magnetic Field Around a Long Straight Wire

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