---
title: "Permeability of Free Space (μ₀) — AP Physics 2 Definition"
description: "Permeability of free space (μ₀ = 4π×10⁻⁷ T·m/A) links current to magnetic field in B = μ₀I/(2πr). Learn how it shows up in AP Physics 2 Unit 12."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/permeability-of-free-space"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 12"
---

# Permeability of Free Space (μ₀) — AP Physics 2 Definition

## Definition

The permeability of free space (μ₀ = 4π × 10⁻⁷ T·m/A) is the fundamental constant that converts electric current into magnetic field strength in a vacuum, appearing in the AP Physics 2 equation B = μ₀I/(2πr) for the field around a long, straight, current-carrying wire.

## What It Is

The permeability of free space, written μ₀ ("mu naught"), is a [fundamental](/ap-physics-2-revised/unit-14/6-wave-interference-and-standing-waves/study-guide/3twkmfrYKPDOuep9 "fv-autolink") physical constant equal to 4π × 10⁻⁷ T·m/A. It answers a simple question. If you push a certain amount of current through a wire, how strong is the magnetic field it creates? μ₀ is the conversion factor. Think of it as nature's exchange rate between amps and teslas.

In [AP Physics 2](/ap-physics-2-revised "fv-autolink"), μ₀ lives inside the equation B = μ₀/(2π) (I/r), which gives the magnetic field magnitude a perpendicular distance r from a long, straight wire carrying current I. The field wraps around the wire in concentric circles ([right-hand rule](/ap-physics-2-revised/key-terms/right-hand-rule "fv-autolink")), gets stronger with more current, and weaker as you move away. μ₀ is what sets the overall scale. The "free space" part means vacuum, though air is so close to vacuum magnetically that you treat them the same on the exam.

## Why It Matters

μ₀ sits at the heart of Topic 12.3 (Magnetism and Current-Carrying Wires) in [Unit 12](/ap-physics-2-revised/unit-12 "fv-autolink"). Learning objective 12.3.A asks you to describe the magnetic field produced by a current-carrying wire, and the essential knowledge hands you the equation B = μ₀/(2π) (I/r) directly. Without μ₀, you can describe the field's shape and direction, but you can't calculate its actual magnitude. The constant is also the bridge in two-wire problems. Wire 1 creates a field using μ₀ (LO 12.3.A), and that field then pushes on wire 2 through [F_B = IℓB sin θ](/ap-physics-2-revised/key-terms/f-b-ilb-sin "fv-autolink") (LO 12.3.B). Conceptually, μ₀ is also evidence for one of the biggest ideas in the course, that electricity and magnetism are two faces of the same interaction. A single constant ties moving charge to magnetic field.

## Connections

### [B = μ₀/(2π) (I/r) (Unit 12)](/ap-physics-2-revised/key-terms/b-0-2-i-r)

This is μ₀'s home equation. The constant sets the scale, the [current](/ap-physics-2-revised/unit-11/1-electric-current/study-guide/QaFR8etPqRmh5pdg "fv-autolink") I cranks the field up, and the distance r dilutes it. Everything else in the formula is geometry; μ₀ is the physics.

### [F_B = IℓB sin θ (Unit 12)](/ap-physics-2-revised/key-terms/f-b-ilb-sin)

Chain these two equations together for parallel-wire problems. One wire's current makes a field (that's where μ₀ enters), and that field exerts a force on the second wire. Parallel currents attract, antiparallel currents repel.

### Permittivity of free space, ε₀ (Unit 10)

ε₀ is μ₀'s electric twin. It sets the strength of the electric force between charges in [Coulomb's law](/ap-physics-2-revised/key-terms/coulombs-law "fv-autolink"), the same way μ₀ sets the strength of the magnetic field from a current. The deep payoff is that the two constants together determine the speed of light, since c = 1/√(μ₀ε₀).

## On the AP Exam

μ₀ shows up almost entirely through B = μ₀/(2π) (I/r). Multiple-choice questions ask you to identify what μ₀ stands for in the formula, calculate B given I and r, solve backward for μ₀ from measured field data, or pick out which factors do and don't affect field strength (hint: μ₀ is a constant, so it's never the variable changing the field). The good news is you don't memorize the value; μ₀ is on the AP Physics 2 constants sheet. In free-response settings, μ₀ powers any quantitative claim about field strength near a wire, and proportional reasoning is the favorite move. Double the current and B doubles. Double the distance and B halves. No released FRQ hinges on the constant by name, but any wire-field calculation runs through it.

## permeability of free space vs Permittivity of free space (ε₀)

Permeability (μ₀) is magnetic; permittivity (ε₀) is electric. μ₀ relates current to the magnetic field it produces and equals 4π × 10⁻⁷ T·m/A. ε₀ relates charge to the electric force and field it produces, hiding inside Coulomb's constant k = 1/(4πε₀). A quick memory hook is that 'permeability' and 'magnetic' both describe how field lines pass through (permeate) space around a current. If the equation has I, you want μ₀; if it has q, you want ε₀.

## Key Takeaways

- The permeability of free space, μ₀ = 4π × 10⁻⁷ T·m/A, is the constant that converts current into magnetic field strength in a vacuum or air.
- μ₀ appears in B = μ₀/(2π) (I/r), the equation for the magnetic field a distance r from a long, straight wire carrying current I.
- Because μ₀ is a constant, only current and distance actually change the field strength around a wire; B is proportional to I and inversely proportional to r.
- You don't need to memorize μ₀'s value since it's provided on the AP Physics 2 reference sheet, but you do need to recognize what it means in an equation.
- Don't mix up μ₀ (permeability, magnetic, goes with current) and ε₀ (permittivity, electric, goes with charge).
- In two-wire problems, μ₀ enters when one wire's current creates a field, and F_B = IℓB sin θ then gives the force that field exerts on the other wire.

## FAQs

### What is the permeability of free space in AP Physics 2?

It's the constant μ₀ = 4π × 10⁻⁷ T·m/A that relates the [magnetic field](/ap-physics-2-revised/unit-12/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ "fv-autolink") around a current-carrying wire to the current producing it. It appears in the Topic 12.3 equation B = μ₀/(2π) (I/r).

### Do I have to memorize the value of μ₀ for the AP exam?

No. μ₀ is listed on the AP Physics 2 constants and equations sheet you get during the exam. What you actually need is to recognize it in B = μ₀/(2π) (I/r) and use it correctly in calculations.

### What's the difference between permeability (μ₀) and permittivity (ε₀)?

μ₀ is the magnetic constant, linking current to magnetic field, while ε₀ is the electric constant, linking charge to electric force in Coulomb's law. If the formula involves current I, you're using μ₀; if it involves charge q, you're using ε₀.

### Does μ₀ change the magnetic field strength around a wire?

No, μ₀ is a fixed constant, so it never changes. In B = μ₀/(2π) (I/r), only the current I and the perpendicular distance r actually vary the field strength, which is exactly the kind of distinction multiple-choice questions test.

### Why is μ₀ written as 4π × 10⁻⁷ instead of a decimal?

Because the 4π form cancels neatly with the 2π in B = μ₀/(2π) (I/r), leaving 2 × 10⁻⁷ T·m/A out front. That makes mental math on the exam much faster. As a decimal it's about 1.26 × 10⁻⁶ T·m/A.

## Related Study Guides

- [12.3 Magnetism and Current-Carrying Wires](/ap-physics-2-revised/unit-12/3-magnetism-and-current-carrying-wires/study-guide/TzaJHQDjTp5y8iuQ)

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