Magnetic Flux Calculator

Magnetic flux measures the total amount of magnetic field passing through a given area. For a uniform field B through a flat surface of area A:

$$\Phi = \vec{B} \cdot \vec{A} = BA\cos\theta$$

Here, θ is the angle between the magnetic field direction and the outward normal to the surface. Important cases:

• θ = 0°: Field perpendicular to surface (maximum flux): $$\Phi = BA$$
• θ = 90°: Field parallel to surface (zero flux): $$\Phi = 0$$
• 0° < θ < 90°: Only the component of B perpendicular to the surface contributes.

The SI unit of magnetic flux is the weber (Wb), where 1 Wb = 1 T·m² = 1 V·s. The CGS unit is the maxwell (Mx), where 1 Wb = 10⁸ Mx.

Faraday's law connects changing flux to induced EMF:

$$\mathcal{E} = -\frac{d\Phi}{dt}$$

This is why magnetic flux is so important: any change in flux — whether from changing B, changing A, or changing θ — induces a voltage. Generators work by rotating a coil (changing θ), transformers by changing B via alternating current, and eddy current brakes by moving a conductor through a field (changing Φ through the conductor).

The calculated flux represents how much magnetic field threads through your surface. When θ = 0°, the surface captures maximum flux. As the surface tilts (θ increases), less flux passes through. At θ = 90°, no net flux passes through — the field skims along the surface. In electromagnetic induction, it is the rate of change of this flux that produces an EMF.