1. Concept Overview
Whenever I imagine a magnetic field passing through any surface, I like to think of it as invisible lines entering or leaving the surface. Magnetic flux is simply a measure of how many of these magnetic field lines pass through that surface.
If more field lines pass through, the flux is larger. If fewer lines pass through, the flux is smaller. The idea is similar to imagining rain falling on a tilted surface — the amount of rain that actually hits depends on how the surface is oriented and how strong the rainfall is.
1.1. Key idea I keep in mind
The flux depends on three things: the magnetic field strength (B), the area (A), and the angle between them (θ). So even if the field is strong, the flux can be zero if the surface is turned sideways.
2. What Magnetic Flux Means Mathematically
The formula that captures the meaning of magnetic flux for a flat surface in a uniform magnetic field is:
\( \Phi_B = B A \cos\theta \)
This expression is simple yet very useful because it tells me exactly how flux behaves when I change the area or orientation of the surface.
2.1. Understanding each term
- B is the magnetic field strength.
- A is the area of the surface through which the field lines pass.
- θ is the angle between the magnetic field and the normal (perpendicular direction) to the surface.
This angle θ is what often gets confusing, so I remind myself: never take the angle between the field and the surface itself — always take the angle between the field and the perpendicular to the surface.
2.2. When flux becomes maximum or minimum
- Flux is maximum when the magnetic field is exactly perpendicular to the surface (\(\theta = 0^\circ\)), because \( \cos 0 = 1 \).
- Flux is zero when the field is parallel to the surface (\(\theta = 90^\circ\)), because \( \cos 90 = 0 \).
This is exactly like rain falling on a tilted roof — the amount hitting the roof depends on the tilt.
3. Magnetic Flux Through Non-Uniform Fields
The formula \(\Phi_B = B A \cos\theta\) works perfectly for a uniform field over a flat area. But if the field is not uniform or the surface is curved, I need to think in smaller parts.
In this case, magnetic flux is defined using an integral:
\( \Phi_B = \int \vec{B} \cdot d\vec{A} \)
Even though this looks complicated, I think of it as breaking the surface into tiny pieces where the field is almost uniform, calculating small flux contributions, and adding them all together.
3.1. Meaning of the dot product here
The dot product \(\vec{B} \cdot d\vec{A}\) simply means we are considering only the component of \(\vec{B}\) that is perpendicular to that tiny area element. This matches the intuition that magnetic flux counts how many field lines pass through, not along, the surface.
4. Units and Dimensions
Magnetic flux is measured in weber (Wb) in SI units. Another commonly used unit is the maxwell (CGS), but the weber is standard in modern physics.
4.1. Units I note down
- 1 weber (Wb) = 1 tesla × 1 m²
- Dimensions of flux: \( [M^1 L^2 T^{-2} I^{-1}] \)
5. How I Visualise Magnetic Flux
Instead of memorising formulas, I find it easier to imagine a simple loop placed in a magnetic field. The number of field lines that actually pass through the loop gives the flux.
5.1. Three simple visual cases
- Case 1: Field is perpendicular to the loop → maximum lines pass through → flux is maximum.
- Case 2: Field is at some angle → fewer lines pass → flux decreases but is not zero.
- Case 3: Field is parallel to the plane of the loop → almost no lines pass → flux is zero.
5.2. Why I find this helpful
Many problems in electromagnetic induction or AC generators become simpler if I first sketch the loop and the direction of the field. Once this picture is clear, the flux behaviour becomes obvious.
6. Physical Feel of Flux Change
Magnetic flux itself is not directly responsible for induction — it is the change in flux that matters. The moment flux through a loop starts increasing or decreasing, an induced emf appears.
This idea will play a bigger role in electromagnetic induction, but I keep a simple note here:
"Changing flux → induced emf"
6.1. How flux changes
Flux can change by:
- changing the magnetic field strength,
- changing the area of the loop,
- changing the orientation of the loop.
This prepares the foundation for understanding Faraday’s law.