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Magnetic Flux Calculator

Find flux Φ = BA cos θ through a loop or surface

Parameters

Tⓘ
m²ⓘ
°ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Magnetic Flux:
0.01;Wb0.01;Wb

Examples

B=0.3 T, A=0.02 m²

θ=0.

    Visualization

    Magnetic Flux

    Magnetic flux Φ measures how much magnetic field passes through a surface. For uniform B over flat area A, Φ = B⃗·A⃗ = BA cos θ, where θ is the angle between B and the outward normal to the surface (not the angle between B and the plane of the loop). SI unit: weber (Wb); 1 Wb = 1 T·m².

    Maximum flux occurs when the surface is perpendicular to B (normal parallel to B, θ = 0, cos θ = 1). Zero flux when the surface is edge-on to field lines (plane parallel to B, θ = 90°). Tilting a coil in uniform B changes Φ continuously — the basis of AC generators.

    For a coil with N identical turns, flux linkage is λ = NΦ. Faraday's law uses linkage: ε = −dλ/dt = −N dΦ/dt if N is constant.

    Gauss's law for magnetism states net flux through any closed surface is zero (∮B·dA = 0) because magnetic monopoles do not exist — field lines always close on themselves.

    Example: B = 0.3 T through a loop of area 0.02 m² face-on gives Φ = 0.006 Wb = 6 mWb. Rotating the loop 90° drops Φ to zero; changing Φ by 0.006 Wb in 0.1 s through 100 turns would induce |ε| = 6 V.

    Flux is central to transformers (mutual flux linkage), induction cooktops (changing B through metal), and magnetic shielding design.

    Key Concepts

    • Φ = BA cos θ (uniform field)
    • θ = angle to normal
    • 1 Wb = 1 T·m²
    • Linkage λ = NΦ
    • ∮B·dA = 0 (no monopoles)
    • dΦ/dt → induced EMF

    Real-World Applications

    • AC generator flux variation
    • Transformer core flux
    • Faraday coil experiments
    • Magnetic flux gate sensors
    • Class 12 flux and induction

    Explore Further

    More magnetism tools

    Physics Equations

    Flux:
    Φ=BAcos⁡θ\Phi = BA\cos\theta

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Magnetic Flux Definition

    Equation:

    Φ=B⃗⋅A⃗=BAcos⁡θ\Phi = \vec{B}\cdot\vec{A} = BA\cos\theta

    Explanation:

    θ is angle between B and the normal (perpendicular) to the surface.

    2

    Step 2: Identify θ

    Calculation:

    θ=0°⇒cos⁡θ=1.0000\theta = 0° \Rightarrow \cos\theta = 1.0000

    Explanation:

    θ = 0° (face ⊥ B) gives maximum flux; θ = 90° gives zero.

    3

    Step 3: Given B and A

    Result:

    B=0.3 T,A=0.02 m2B = 0.3\ \text{T},\quad A = 0.02\ \text{m}^2
    4

    Step 4: Compute Flux

    Calculation:

    Φ=0.3×0.02×1.0000=6.0000e−3 Wb\Phi = 0.3 \times 0.02 \times 1.0000 = 6.0000e-3\ \text{Wb}

    Result:

    Φ=6.0000e−3WbΦ = 6.0000e-3 Wb
    5

    Step 5: Units

    1 weber (Wb) = 1 T·m² = 1 V·s.

    Explanation:

    Flux linkage for N turns: NΦ.

    6

    Step 6: Link to Induction

    Equation:

    E=−NdΦdt\mathcal{E} = -N\frac{d\Phi}{dt}

    Explanation:

    Changing flux through a coil induces EMF (Faraday's law).

    Frequently Asked Questions (FAQ)

    Negative flux?

    Sign depends on chosen normal direction.

    Uniform B, tilted loop?

    Use cos θ with area normal.

    Practice MCQs

    1. Magnetic flux:
    2. SI unit of flux:
    3. θ = 90° (plane || B):
    4. Doubling area doubles:
    5. Flux through closed surface:
    6. N turns flux linkage:

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