Magnetic Flux Calculator

Magnetic flux measures how many magnetic field lines pass through a surface. Changing flux induces EMF by Faraday law — the foundation of all generators and transformers.

🧲 Electromagnetism📐 Φ = BAcosθ⚡ Faraday Law
B Field (T)
Area (m²)
Angle θ (deg, between B and surface normal)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Magnetic FluxΦΦ = B A cosθWb (Weber)
B FieldBB = Φ/(A cosθ)T (Tesla)
AreaAA = Φ/(B cosθ)m²
AngleθBetween B and surface normaldeg
1 Weber1 Wb= 1 V·s = 1 T·m²—

Step-by-Step Examples

Example 1
Coil in Magnetic Field

Circular coil r=5 cm, B=0.3 T, theta=0 (perpendicular).

  • A = π(0.05)² = 7.85×10⁻³ m²
  • Φ = 0.3 × 7.85×10⁻³ × cos0° = 2.36 mWb
✓ 2.36 mWb through the coil
Example 2
Tilted Surface

B=0.5 T, A=0.02 m², theta=60°.

  • Φ = 0.5 × 0.02 × cos60° = 0.01 × 0.5 = 5 mWb
✓ 5 mWb — less than perpendicular case
Example 3
Earth Magnetic Flux

Earth B = 50 μT, coil A = 1 m², theta = 0.

  • Φ = 50×10⁻⁶ × 1 × 1 = 50 μWb
✓ 50 microwebers — used in magnetometers

Real-World Applications

🔌
Transformers
Maximizing flux through core transfers energy between windings via Faraday law.
📱
Wireless Charging
Coil alignment maximizes magnetic flux linkage for efficient power transfer.
🚗
Position Sensors
Flux detectors measure rotating components in motors and ABS wheel speed sensors.
🏺
MRI Machines
Superconducting coils maintain precise, uniform flux for medical imaging.

Common Mistakes to Avoid

⚠️
Confusing flux with field

B is field strength (T). Flux Phi = BA cos theta (Wb) depends on area and orientation.

⚠️
Forgetting cosine factor

Only B perpendicular to surface contributes. Parallel B gives zero flux.

⚠️
Angle convention

Theta is between B and the surface NORMAL (perpendicular to surface), not the surface itself.

Frequently Asked Questions

What is 1 Weber? ▾
1 Wb = 1 V*s = 1 T*m^2. A flux of 1 Wb collapsing to 0 in 1 second induces 1 V in a single-turn coil.
Can flux be negative? ▾
Yes. If B reverses relative to the defined surface normal, cos(theta) > 90 degrees gives negative flux. Sign determines direction of induced EMF.
What is flux linkage? ▾
For N-turn coil: Lambda = N*Phi (Wb-turns). EMF = -dLambda/dt. Flux linkage accounts for all turns.
Why is divergence of B always zero? ▾
Gauss law for magnetism: div(B) = 0, meaning magnetic flux through any closed surface is zero. No magnetic monopoles exist.
How does flux relate to inductance? ▾
L = N*Phi/I. Inductance is flux linkage per unit current. Self-inductance arises from the coil own changing current.
What is flux in a transformer core? ▾
AC flux Phi = Phi_max * sin(2*pi*f*t). Induced EMF = -N * d Phi/dt = -N * Phi_max * 2*pi*f * cos(2*pi*f*t).
What is Earth total magnetic flux? ▾
Earth surface area ~5.1e14 m^2, average B ~50 uT, gives total flux ~2.55e10 Wb. Changes in this drive geomagnetically induced currents.
How is flux measured experimentally? ▾
Using a Hall probe, search coil (measure EMF from known flux change), or SQUID magnetometer for tiny flux quanta.

Related Physics Calculators

⚡ Faraday Law📡 Inductance🧲 Magnetic Field⚡ Electric Flux🧲 Magnetic Force

Formula Explorer connections

Interpretation: This relationship connects magnetic fields, moving charge, flux, induction or electromagnetic material response. Assumption: Specify field direction and sign convention. Uniform fields, linear materials, negligible edge effects or sinusoidal steady state may be assumed.

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