IB Physics Topic D.4.1 Principles of Electromagnetic Induction Revision Notes (HL)

IB Physics Topic D.4.1 Principles of Electromagnetic Induction Revision Notes (HL) | RevisionDojo

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Magnetic Flux: A Measure of Magnetic Field Through a Surface

Definition

Magnetic flux

Magnetic flux $\Phi$ quantifies the amount of magnetic field passing through a given surface.

It is defined as:

$$\Phi = BA \cos \theta$$

where:

$B$ is the magnetic flux density (measured in teslas, T).
$A$ is the area of the surface (measured in square meters, $\text{m}^2$).
$\theta$ is the angle between the magnetic field lines and the normal (perpendicular) to the surface.

Tip

The unit of magnetic flux is the weber (Wb), where $1 \text{ Wb} = 1 \text{ T} \cdot \text{m}^2$.

Understanding the Formula

When the field is perpendicular to the surface $(\theta = 0^\circ)$, the flux is maximized: $$\Phi = BA$$
When the field is parallel to the surface $(\theta = 90^\circ)$, the flux is zero: $$\Phi = 0$$
For angles in between, the flux is reduced by the factor $\cos \theta$.

Example question

A loop of area $0.1 \, \text{ m}^2$ is placed in a uniform magnetic field of $0.5 \, \text{ T}$. Calculate the magnetic flux through the loop when:

The loop is perpendicular to the field.
The loop is at an angle of $60^\circ$ to the field.

Solution

Perpendicular $(\theta = 0^\circ)$:

$$\Phi = BA \cos \theta$$

$$ = 0.5 \times 0.1 \times \cos 0^\circ = 0.05 \text{ Wb}$$

At $60^\circ$:

$$\Phi = BA \cos \theta $$

$$= 0.5 \times 0.1 \times \cos 60^\circ = 0.025 \text{ Wb}$$

What Causes the Magnetic Flux to Change?

Changing the magnetic flux density B through the loop.
Changing the area A of the surface that sits inside the field.
Changing the angle between the field and the normal to the loop, for example by rotating the coil.
A stationary magnet or a steady field induces no emf, because only a changing flux produces one.

Faraday’s Law: Inducing Emf Through Changing Magnetic Flux

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Magnetic Flux: A Measure of Magnetic Field Through a Surface

Definition

Magnetic flux

Magnetic flux $\Phi$ quantifies the amount of magnetic field passing through a given surface.

It is defined as:

$$\Phi = BA \cos \theta$$

where:

$B$ is the magnetic flux density (measured in teslas, T).
$A$ is the area of the surface (measured in square meters, $\text{m}^2$).
$\theta$ is the angle between the magnetic field lines and the normal (perpendicular) to the surface.

Tip

The unit of magnetic flux is the weber (Wb), where $1 \text{ Wb} = 1 \text{ T} \cdot \text{m}^2$.

Understanding the Formula

When the field is perpendicular to the surface $(\theta = 0^\circ)$, the flux is maximized: $$\Phi = BA$$
When the field is parallel to the surface $(\theta = 90^\circ)$, the flux is zero: $$\Phi = 0$$
For angles in between, the flux is reduced by the factor $\cos \theta$.

Example question

A loop of area $0.1 \, \text{ m}^2$ is placed in a uniform magnetic field of $0.5 \, \text{ T}$. Calculate the magnetic flux through the loop when:

The loop is perpendicular to the field.
The loop is at an angle of $60^\circ$ to the field.

Solution

Perpendicular $(\theta = 0^\circ)$:

$$\Phi = BA \cos \theta$$

$$ = 0.5 \times 0.1 \times \cos 0^\circ = 0.05 \text{ Wb}$$

At $60^\circ$:

$$\Phi = BA \cos \theta $$

$$= 0.5 \times 0.1 \times \cos 60^\circ = 0.025 \text{ Wb}$$

What Causes the Magnetic Flux to Change?

Changing the magnetic flux density B through the loop.
Changing the area A of the surface that sits inside the field.
Changing the angle between the field and the normal to the loop, for example by rotating the coil.
A stationary magnet or a steady field induces no emf, because only a changing flux produces one.

Faraday’s Law: Inducing Emf Through Changing Magnetic Flux

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics D.4.1 Principles of Electromagnetic Induction Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Magnetic Flux: A Measure of Magnetic Field Through a Surface

Understanding the Formula

What Causes the Magnetic Flux to Change?

Faraday’s Law: Inducing Emf Through Changing Magnetic Flux

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Magnetic Flux: A Measure of Magnetic Field Through a Surface

Understanding the Formula

What Causes the Magnetic Flux to Change?

Faraday’s Law: Inducing Emf Through Changing Magnetic Flux

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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