Hong Life CalculatorsUnderstanding the magnetic flux converter — concept and principle
Magnetic flux, written Φ, is the total amount of magnetic field passing through a surface. Where flux density B tells you how strong the field is at a point, flux tells you how much field threads through a whole area, such as the cross-section of a transformer core or the loop of a coil. It is the quantity that appears in Faraday's law of induction, so it matters for transformers, generators, inductors and magnetic sensors. This converter switches between the SI weber (Wb), its milli- and micro- forms, and the CGS maxwell (Mx).
How it is calculated
Values are converted to webers and then to the target unit: result = value × (Wb per "from" unit) ÷ (Wb per "to" unit). All factors are exact:
- 1 mWb = 10⁻³ Wb
- 1 µWb = 10⁻⁶ Wb
- 1 Mx = 10⁻⁸ Wb, so 1 Wb = 100,000,000 Mx
To find flux from a field, use Φ = B × A × cos θ, with B in tesla, A in square metres and θ the angle between the field and the surface's normal.
The principle
Picture magnetic field lines passing through a window. Flux counts how many lines go through: a stronger field or a bigger window gives more flux, and tilting the window lets fewer lines through, hence the cos θ. One weber is the flux of a 1 T field crossing 1 m² at right angles. The weber is also linked to voltage: by Faraday's law, the voltage induced in one turn of wire equals the rate of change of flux, so a change of 1 Wb in 1 s induces 1 V. That is why 1 Wb = 1 V·s. In the CGS system, 1 Mx is the flux of 1 G through 1 cm²; since 1 G = 10⁻⁴ T and 1 cm² = 10⁻⁴ m², 1 Mx = 10⁻⁸ Wb.
Worked example
- Inputs: value = 1, from webers, to milliwebers.
- 1 Wb × 1 ÷ 0.001 = 1,000 mWb.
- In other units: 1,000,000 µWb and 100,000,000 Mx.
How to read the result
A weber is a large flux for small devices. A transformer core with a 10 cm² cross-section (0.001 m²) running at a peak flux density of 1.5 T carries a peak flux of 1.5 × 0.001 = 1.5 mWb. Sensor and small-coil work is often in microwebers, while older magnet literature quotes maxwells, sometimes in thousands or millions.
Common mistakes
- Confusing flux (Wb) with flux density (T = Wb/m²). You need the area to go from one to the other.
- Forgetting to convert the area to square metres; 1 cm² is 10⁻⁴ m², not 10⁻² m².
- Ignoring the angle; a surface parallel to the field has zero flux through it.
Frequently asked questions
How many maxwells are in one weber?
Exactly 100,000,000 (10⁸) Mx.
Why is the weber equal to a volt-second?
Faraday's law says the induced voltage in a loop equals the rate of change of flux through it. A change of 1 Wb over 1 s gives 1 V, so 1 Wb = 1 V·s.
What is a "line" of magnetic flux?
In older literature, one line equals one maxwell, so 10⁸ lines make 1 Wb.
Sources: BIPM, The International System of Units (SI Brochure), 9th edition, 2019 · NIST Special Publication 811 (2008), Appendix B · D. J. Griffiths, Introduction to Electrodynamics, Cambridge University Press