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Faraday's Law — Induced EMF

Find |ε| = N |ΔΦ/Δt| from flux change in a coil

Parameters

ⓘ
Wbⓘ
sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Induced EMF (magnitude):
10.00;V10.00;V

Examples

N=100, ΔΦ=0.01 Wb in 0.1 s

Quick change.

    Visualization

    Faraday's Law of Electromagnetic Induction

    Faraday's law states that a changing magnetic flux through a coil induces an electromotive force ε = −N dΦ/dt, where N is the number of turns and Φ is flux through each turn. The minus sign is Lenz's law: the induced current (if the circuit is closed) creates a magnetic field that opposes the change in flux that caused it.

    For a finite change over time interval Δt, magnitude |ε| ≈ N|ΔΦ/Δt|. Example: N = 100, ΔΦ = 0.01 Wb in Δt = 0.1 s gives |ε| = 10 V — enough to light a small LED briefly if the coil resistance is low.

    Flux can change because B changes, area changes, orientation changes, or the coil moves into/out of a field region. Dropping a magnet through a coil increases then decreases Φ, producing a bipolar voltage pulse.

    Motional EMF is an equivalent viewpoint: a conductor of length l moving at speed v perpendicular to B experiences magnetic force on charges that separates them, producing ε = Blv along the rod. This explains rail generators and MHD concepts.

    Eddy currents are induced in bulk conductors (metal plates, braking disks) when flux changes; they dissipate energy as heat — used in induction furnaces and magnetic brakes, undesired in transformer cores (lamination reduces them).

    Transformers, AC generators, induction cooktops, wireless charging pads, and bicycle dynamos all depend on Faraday + Lenz. Class 12 EMI chapter is built on this law.

    Key Concepts

    • ε = −N dΦ/dt
    • Lenz: induced effect opposes ΔΦ
    • |ε| = N|ΔΦ/Δt| (uniform rate)
    • Motional EMF ε = Blv
    • Eddy currents in conductors

    Real-World Applications

    • AC generators and dynamos
    • Transformers (mutual induction)
    • Induction cooking and forging
    • Eddy-current brakes
    • Wireless charging
    • Class 12 EMI numericals

    Explore Further

    More magnetism tools

    Physics Equations

    Faraday:
    E=−NΔΦΔt\mathcal{E} = -N\frac{\Delta\Phi}{\Delta t}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Faraday's Law

    Equation:

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

    Explanation:

    Induced EMF equals negative rate of change of flux linkage.

    2

    Step 2: Finite Change

    Equation:

    ∣E∣≈N∣ΔΦΔt∣|\mathcal{E}| \approx N\left|\frac{\Delta\Phi}{\Delta t}\right|

    Explanation:

    Use when Φ changes uniformly over interval Δt.

    3

    Step 3: Flux Rate

    Calculation:

    ΔΦΔt=0.010.1=1.0000e−1 Wb/s\frac{\Delta\Phi}{\Delta t} = \frac{0.01}{0.1} = 1.0000e-1\ \text{Wb/s}

    Result:

    dΦ/dt=1.0000e−1Wb/sdΦ/dt = 1.0000e-1 Wb/s
    4

    Step 4: Induced EMF

    Calculation:

    ∣E∣=100×1.0000e−1=10.000000 V|\mathcal{E}| = 100 \times 1.0000e-1 = 10.000000\ \text{V}

    Result:

    ∣ε∣=10.000000V|ε| = 10.000000 V
    5

    Step 5: Lenz's Law (Sign)

    Induced current creates B that opposes the change in flux.

    Explanation:

    The minus sign in ε = −NdΦ/dt encodes Lenz's law.

    6

    Step 6: Examples

    Moving magnet toward coil increases Φ → induced I repels magnet.

    Explanation:

    Generators rotate coil in B to produce alternating EMF.

    Frequently Asked Questions (FAQ)

    Sign of ε?

    Lenz: induced current creates B opposing flux change.

    Constant Φ?

    No induced EMF if flux not changing.

    Practice MCQs

    1. Faraday law:
    2. Lenz law says induced current:
    3. Faster flux change:
    4. More turns N:
    5. Generator converts:
    6. Transformer uses:

    Related Calculators

    These tools connect to the same physics concepts used in this calculator.

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