Magnetic Flux Calculator (Φ = BA cosθ)
Magnetic flux measures how much magnetic field passes through a surface. It is the foundation of electromagnetic induction: changing flux through a coil is what generates voltage in generators, transformers, and wireless chargers. This calculator finds the flux from field strength, area, and the angle between the field and the surface.
The Formula
Phi = B x A x cos(theta)
Where B is the magnetic field in Tesla, A is the area of the surface in m squared, and theta is the angle between the field direction and the line perpendicular to the surface (the surface normal).
Understanding the Angle
- theta = 0 degrees: Field is perpendicular to the surface. Maximum flux. This is a coil face-on to the field.
- theta = 90 degrees: Field runs parallel to the surface. Zero flux. No field lines pass through.
- theta = 45 degrees: Flux is reduced by cos(45) = 0.707, about 71% of maximum.
Magnetic Field Strengths
| Source | Strength |
|---|---|
| Earth's magnetic field | ~25-65 uT |
| Refrigerator magnet | 5 mT |
| Bar magnet (surface) | 10-100 mT |
| Neodymium magnet | 0.2-1.4 T |
| MRI scanner | 1.5-3 T |
| Large electromagnet | 1-20 T |
Why Magnetic Flux Matters
Faraday's law says the voltage induced in a coil equals the rate of change of magnetic flux: EMF = -d(Phi)/dt. This is the operating principle behind every electric generator, transformer, and induction cooktop. Understanding flux is the first step to understanding all of electromagnetic induction.
Units: The Weber
One Weber (Wb) equals one Tesla times one square meter. Named after Wilhelm Eduard Weber, it is the SI unit of magnetic flux. In everyday applications, milliwebers (mWb) and microwebers (uWb) are more common since most surfaces and fields are small.