Magnetic Flux Calculator
Calculate magnetic flux using the formula Phi = B times A times cos(theta).
Enter field strength, surface area, and angle to find total flux in webers.
Magnetic Flux
How Magnetic Flux Is Calculated
Magnetic flux measures the total magnetic field passing through a given surface area. It determines how much of the magnetic field is “captured” by a loop or coil, which drives electromagnetic induction.
Magnetic Flux Formula:
Φ = B × A × cos(θ)
Where:
- Φ (Phi) = magnetic flux in Webers (Wb)
- B = magnetic field strength in Tesla (T)
- A = area of the surface in square meters (m²)
- θ (theta) = angle between the magnetic field direction and the normal to the surface
Special Cases:
- θ = 0° (field perpendicular to surface): Φ = B × A (maximum flux)
- θ = 90° (field parallel to surface): Φ = 0 (no flux passes through)
Worked Example: A circular coil with radius 0.05m is placed in a 0.3 T magnetic field at 30° to the normal:
- A = π × (0.05)² = 7.854 × 10⁻³ m²
- cos(30°) = 0.866
- Φ = 0.3 × 7.854 × 10⁻³ × 0.866 = 2.04 × 10⁻³ Wb = 2.04 mWb
Faraday’s Law Connection:
A changing magnetic flux induces a voltage:
EMF = −N × ΔΦ/Δt
where N is the number of coil turns. This is the operating principle of generators and transformers.
Typical Field Strengths:
- Earth’s magnetic field: ~50 µT (0.00005 T)
- Refrigerator magnet: ~0.01 T
- MRI machine: 1.5–3.0 T
- Neodymium magnet: 1.0–1.5 T