PhysicsMagnetismA-Level

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Flux

Magnetic flux through an area.

Understand the formulaSee the free derivationOpen the full walkthrough

Φ = B A

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Core idea

Overview

Magnetic flux is a measurement of the total magnetic field passing through a specific surface area. In this fundamental form, it assumes a uniform magnetic field lines up perpendicularly to the surface plane.

When to use: This formula applies when the magnetic field B is constant over the entire area A. It is specifically used when the angle between the magnetic field and the surface normal is zero degrees, meaning the field is perpendicular to the surface.

Why it matters: Understanding flux is essential for Faraday's Law, which explains how moving magnets generate electricity in power plants. It is the core principle behind the operation of transformers, electric motors, and induction chargers.

Symbols

Variables

B = Magnetic Flux Density, A = Area, \Phi = Magnetic Flux

B

Magnetic Flux Density

T

A

Area

m^{2}

Φ

Magnetic Flux

W b

Walkthrough

Derivation

Understanding Magnetic Flux

Quantifies the total magnetic field passing through a given area.

The magnetic field B is uniform over the area A.

State the Definition:

Flux equals B times area A, multiplied by cos $θ$ where $θ$ is the angle between B and the area’s normal.

Φ = B A cos θ

Result

Φ = B A cos θ

Source: OCR A-Level Physics A — Electromagnetism

Free formulas

Rearrangements

Solve for $Φ$

Make Phi the subject

Φ = B A

Phi is already the subject of the formula.

Difficulty: 1/5

Solve for $B$

Make B the subject of the Flux equation

B = \frac{Φ}{A}

Rearrange the magnetic flux equation to solve for magnetic flux density (B).

Difficulty: 2/5

Solve for $A$

Make A the subject

A = \frac{Φ}{B}

Start from Flux. To make A the subject, divide by B.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin because Phi is directly proportional to B. For a physics student, this means that a larger magnetic flux density results in a proportionally larger magnetic flux through the same area, while a smaller density results in less flux. The most important feature is that the linear relationship means doubling B will always double Phi. This constant rate of change confirms that the area remains fixed throughout the observation.

Graph type: linear

Why it behaves this way

Intuition

Imagine magnetic field lines as parallel arrows uniformly passing straight through a flat, rectangular window. The magnetic flux is the product of the density of these arrows and the window's area.

Φ

Magnetic flux

The total 'amount' of magnetic field lines passing perpendicularly through a specific surface area. Imagine counting how many magnetic field lines pierce through a given window.

Magnetic field strength (or magnetic flux density)

How strong or dense the magnetic field is. A higher B means more magnetic field lines are packed into a given space.

Area

The size of the surface through which the magnetic field passes. A larger area can 'catch' more magnetic field lines.

Free study cues

Insight

Canonical usage

In the International System of Units (SI), magnetic flux density (B) is expressed in Tesla (T), area (A) in square meters ( $m^{2}$ ), resulting in magnetic flux (Φ) in Weber (Wb).

Common confusion

A common mistake is using non-SI units for magnetic flux density (e.g., Gauss) or area (e.g., $c m^{2}$ ) without proper conversion to Tesla and $m^{2}$ , leading to incorrect flux values in Weber.

Unit systems

$Φ$ Weber (Wb) · Magnetic flux is a scalar quantity representing the total magnetic field passing through a given area.

$B$ Tesla (T) · Magnetic flux density, also commonly referred to as magnetic field strength in introductory contexts.

$A$ square meter (m^2) · The area through which the magnetic field lines pass.

Ballpark figures

Quantity:

One free problem

Practice Problem

A circular wire loop has a surface area of 0.05 m². If a constant magnetic field of 0.4 Tesla passes perpendicularly through the loop, what is the resulting magnetic flux?

Magnetic Flux Density0.4 T

Area0.05 m^2

Solve for: $P hi$

Hint: Multiply the magnetic field strength by the cross-sectional area.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Calculating flux through a coil.

Study smarter

Tips

Ensure the area is in square meters (m²) and the field is in Teslas (T).
One Weber (Wb) is equal to one Tesla-meter squared.
If the field is not perpendicular, remember that flux decreases as the angle increases.

Avoid these traps

Common Mistakes

Using total surface area instead of projected area.
Mixing cm² and m².

Common questions

Frequently Asked Questions

Quantifies the total magnetic field passing through a given area.

This formula applies when the magnetic field B is constant over the entire area A. It is specifically used when the angle between the magnetic field and the surface normal is zero degrees, meaning the field is perpendicular to the surface.

Understanding flux is essential for Faraday's Law, which explains how moving magnets generate electricity in power plants. It is the core principle behind the operation of transformers, electric motors, and induction chargers.

Using total surface area instead of projected area. Mixing cm² and m².