Formula & Calculator
Magnetic Flux
Calculates the magnetic flux through a surface from the magnetic field strength, area, and the angle between the field and the surface's normal.
Interpretation
Magnetic flux: Φ = B·A·cosθ, where B is magnetic field, A is area, θ is angle between field and normal. It measures total magnetic field through a surface. Example: B=0.5 T, A=0.1 m², θ=0 → Φ=0.05 Wb.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Phi | Magnetic flux | Wb |
| B | Magnetic field strength | T |
| A | Area of the surface | m2 |
| theta | Angle between the field and the surface's normal | degrees |
What it means
Magnetic flux (Φ) is a measure of the total magnetic field passing through a given surface. It is the product of the magnetic field strength B, the area A, and the cosine of the angle between B and the normal to the surface. Flux is a scalar quantity measured in webers (Wb). It is central to Faraday’s law of induction: a changing magnetic flux induces an electromotive force (EMF). This principle is the basis for generators, transformers, and electric motors. Flux is also used in magnetic circuit analysis (similar to electric current in circuits). Understanding flux is essential for analysing electromagnetic devices and for studying the behaviour of magnetic materials.
Worked example
Magnetic Flux – Two Examples
Real‑World| Parameter | Value |
|---|---|
| B | 0.5 T |
| A | 0.1 m² |
| θ | 0° |
| Parameter | Value |
|---|---|
| B | 1 T |
| A | 0.2 m² |
| θ | 60° |
Common mistakes
- Magnetic flux Φ: Scalar – but has sign depending on orientation.
- Magnetic field B: In teslas (T) – uniform over the area for this simple formula.
- Area A: In m² – the surface area.
- Angle θ: The angle between the magnetic field and the normal to the surface.
- Units: B·A·cosθ gives weber (Wb) = T·m².
Applications
Magnetic flux, Φ = B·A·cosθ, is the measure of the magnetic field passing through a surface. It is fundamental to electromagnetic induction and is used in the design of transformers, motors, generators, and magnetic sensors. Engineers use flux calculations to design magnetic circuits, to optimise transformer efficiency, and to evaluate the performance of inductors. In geophysics, magnetic flux is used in surveying. In medical imaging, MRI relies on controlled magnetic fields. By understanding magnetic flux, professionals can design efficient electromagnetic devices and interpret magnetic field measurements in various applications.
- Design of transformers, inductors, and electric motors
- Magnetic circuit analysis in relays and actuators
- Geophysical surveying and magnetometry
- Medical MRI and magnetic particle imaging
- Energy harvesting from magnetic fields
Frequently Asked Questions
Magnetic flux (Φ) is a measure of the magnetic field passing through a surface. It is defined as Φ = B·A·cosθ, where B is the magnetic flux density (magnetic field strength), A is the area of the surface, and θ is the angle between the magnetic field and the normal to the surface.
In SI, the unit is the weber (Wb), which is T·m². 1 Wb = 1 V·s.
Using the angle between the field and the surface plane, instead of the angle between the field and the normal. The correct angle is θ with the normal.
Faraday's law states that a change in magnetic flux induces an electromotive force (EMF). The rate of change of flux determines the induced voltage.
Flux density (B) is the flux per unit area: B = Φ/A. Flux is the total field through an area; B is the field strength at a point.
Tilting the surface increases the angle θ, reducing the flux. Flux is maximum when the surface is perpendicular to B (θ=0°), and zero when parallel (θ=90°).
By Gauss's law for magnetism, the net magnetic flux through any closed surface is zero. This reflects that there are no magnetic monopoles (field lines are continuous).
The total flux linkage is λ = N·Φ, where Φ is the flux through one turn. This is used in Faraday's law for coils (EMF = –dλ/dt).