Understanding Magnetic Flux Revision Notes | A Level AQA Physics

1. Why Magnetic Flux Matters

Picture a wire loop held inside a magnetic field. Whether that loop generates an EMF — and how large that EMF is — depends entirely on how much of the field is threading through it. That quantity has a name: magnetic flux.

Magnetic flux is the foundation of electromagnetic induction. Every generator, transformer, and induction motor you will ever analyse at A Level starts here. Get this concept locked in and the rest of the topic follows naturally.

2. Defining Magnetic Flux

Think of magnetic field lines as rain falling vertically. If you hold a flat tray horizontally, the maximum amount of rain lands in it. Tilt the tray and less rain falls in — even though the rainfall rate (the field) has not changed. Magnetic flux works the same way: it measures how much of the field passes through a surface, and that depends on the angle between the field and the surface.

The condition that $B$ is normal to $A$ is critical. The AQA specification defines $\Phi = BA$ specifically for this perpendicular case. When the field is not perpendicular to the area, you need the full cosine version — which we will reach shortly.

3. Flux Linkage for a Multi-Turn Coil

A single loop of wire has flux $\Phi$ passing through it. Now wind that wire into a coil of $N$ turns. Each turn has the same flux threading through it, so the total effect on the coil is $N$ times greater. This total is called the flux linkage.

Flux linkage is what actually drives electromagnetic induction. Faraday's law (which you will meet in the next topic) states that the induced EMF equals the rate of change of flux linkage — so understanding $N\Phi$ is non-negotiable for everything that follows.

4. Flux and Flux Linkage When a Coil Rotates

Here is where the physics becomes genuinely interesting. When a rectangular coil sits in a uniform magnetic field, the flux through it depends on the angle between the field lines and the normal to the coil's plane. As the coil rotates, that angle changes continuously — and so does the flux linkage.

Define $\theta$ as the angle between the magnetic field $B$ and the normal to the plane of the coil. When $\theta = 0°$, the field is perfectly aligned with the normal — the field passes straight through the coil and flux is at its maximum. When $\theta = 90°$, the field runs parallel to the plane of the coil and no field lines thread through it at all — flux is zero.

Notice that $BAN\cos\theta$ reduces to $BAN$ when $\theta = 0°$ (since $\cos 0° = 1$), confirming that $N\Phi = NBA$ is the maximum flux linkage. At $\theta = 90°$, $\cos 90° = 0$ and flux linkage drops to zero. The cosine function captures the full rotation behaviour in one compact expression.

5. Visualising How Flux Linkage Changes with Rotation

Picture a rectangular coil rotating steadily in a uniform field. At the start, the normal to the coil points along the field — maximum flux linkage. As the coil turns through 90°, the normal becomes perpendicular to the field — flux linkage falls to zero. At 180°, the normal points opposite to the field — flux linkage reaches its negative maximum. The pattern is a cosine curve.

The graph confirms the cosine relationship. The flux linkage is positive when the normal has a component along $B$, zero when the coil plane contains $B$, and negative when the normal points opposite to $B$. Examiners frequently ask you to read off values from a graph like this and relate them back to the coil's physical orientation.

Worked example: Calculating Flux Linkage at a Given Angle

A rectangular coil has 150 turns, dimensions 4.0 cm × 6.0 cm, and is placed in a uniform magnetic field of flux density 0.25 T. The normal to the coil makes an angle of 60° with the field direction. Calculate the flux linkage. [3 marks]

1. $N = 150$, $B = 0.25\,\text{T}$, $\theta = 60°$ $A = 4.0\,\text{cm} \times 6.0\,\text{cm} = 0.040\,\text{m} \times 0.060\,\text{m} = 2.4 \times 10^{-3}\,\text{m}^2$ — Convert centimetres to metres before substituting. [M1] for correct identification of the formula and variables.
2. $N\Phi = BAN\cos\theta$ — This is the AQA specification equation for flux linkage at angle $\theta$ between $B$ and the normal to the coil.
3. $\cos 60° = 0.50$ — This is a standard trigonometric value. Confirm: at 60° the flux linkage is half its maximum value.
4. $N\Phi = 0.25 \times 2.4 \times 10^{-3} \times 150 \times 0.50$ — [M1] for correct substitution with consistent SI units.
5. $0.25 \times 2.4 \times 10^{-3} = 6.0 \times 10^{-4}$ $6.0 \times 10^{-4} \times 150 = 9.0 \times 10^{-2}$ $9.0 \times 10^{-2} \times 0.50 = 4.5 \times 10^{-2}\,\text{Wb}$ — Working in stages avoids arithmetic errors. Each multiplication is carried out separately.
6. $N\Phi = 4.5 \times 10^{-2}\,\text{Wb}$ — [A1] for correct answer with correct unit. Weber-turns is acceptable but Wb is standard AQA notation.

Answer: $N\Phi = 4.5 \times 10^{-2}\,\text{Wb}$ (or $0.045\,\text{Wb}$)

6. Worked Comparison: Maximum and Zero Flux Linkage

It is worth pausing to compare the two extreme orientations directly, because examiners often ask you to describe or explain what happens to flux linkage as a coil rotates between them.

The negative value at 180° is physically meaningful: it indicates the field now threads through the coil in the opposite direction compared to the 0° position. This sign change is what drives the alternating nature of the induced EMF in a generator.

7. Exam Technique and Common Pitfalls

Flux and flux linkage questions appear in calculation, describe, and explain formats. The marks are very achievable once you know the traps examiners set. Here is what to watch for.

For extended-response questions asking you to evaluate or explain the behaviour of a rotating coil, structure your answer around three anchor points: the equation $N\Phi = BAN\cos\theta$, the physical geometry at each key angle, and the cosine variation between maximum and zero flux linkage. Examiners award marks for linking the mathematical expression to the physical picture, not for restating the formula alone.

Magnetic flux and flux linkage are the language of electromagnetic induction. Every spec point in this section — from $\Phi = BA$ for a single surface, through $N\Phi$ for a multi-turn coil, to $N\Phi = BAN\cos\theta$ for a rotating coil — builds directly on the same physical idea: how much of the magnetic field threads through the coil, and how that changes with orientation.