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Faraday's Law Calculator

Calculate induced EMF from magnetic flux change in a coil

Parameters

ⓘ
Wbⓘ
sⓘ
Show Trail

Controls

xⓘ

Calculated Values

|Induced EMF|:
50.00;V50.00;V
Flux rate dΦ/dt:
0.50;Wb/s0.50;Wb/s

Examples

100 turns, 0.05 Wb in 0.1 s

Rapid flux change.

  • |Induced EMF|: 50.0050.00

50 turns, 0.01 Wb in 2 s

Slow change.

  • |Induced EMF|: 0.250.25

Visualization

Faraday's Law and Electromagnetic Induction

Faraday's law: the induced EMF in a coil equals the negative rate of change of magnetic flux linkage: ℰ = −N dΦ/dt (SI). Flux linkage = NΦ for N turns.

Magnetic flux Φ = B·A·cosθ = BA cosθ (B in tesla, A in m², θ angle between B and area normal). Changing B, A, or θ induces EMF.

Lenz's law: the minus sign means induced current opposes the flux change that caused it (energy conservation). Direction found with right-hand rule for coils.

Motional EMF: a conductor of length l moving at speed v perpendicular to B has ℰ = Blv. Equivalent to changing flux through the swept area.

Applications: generators rotate coils in B; transformers use changing flux in iron cores; induction cooktops use high-frequency AC fields.

Self-inductance: changing current in a coil induces back-EMF ℰ = −L dI/dt. Inductance L (henry) measures flux linkage per ampere.

Key Concepts

  • ℰ = −N ΔΦ/Δt
  • Φ = BA cosθ
  • Lenz's law — opposes flux change
  • Motional EMF: ℰ = Blv
  • N turns multiply induced EMF
  • Self-inductance: ℰ = −L dI/dt

Real-World Applications

  • AC generators and alternators
  • Transformers (step-up / step-down)
  • Induction motors and cooktops
  • Magnetic stripe and RFID readers
  • Class 12 electromagnetic induction

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Physics Equations

Faraday's Law:
E=−NΔΦΔt\mathcal{E} = -N\frac{\Delta\Phi}{\Delta t}
Flux:
Φ=BAcos⁡θ\Phi = BA\cos\theta

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Flux Change and Time Interval

N turns, change in flux ΔΦ, over time Δt.

Result:

N=100,ΔΦ=0.05 Wb,Δt=0.1 sN = 100, \quad \Delta\Phi = 0.05 \text{ Wb}, \quad \Delta t = 0.1 \text{ s}

Explanation:

Flux Φ = BA cosθ (weber). Change can be from varying B, area A, or angle θ.

2

Step 2: Rate of Flux Change

Equation:

ΔΦΔt\frac{\Delta\Phi}{\Delta t}

Calculation:

ΔΦΔt=0.050.1=0.500000 Wb/s\frac{\Delta\Phi}{\Delta t} = \frac{0.05}{0.1} = 0.500000 \text{ Wb/s}

Result:

dΦ/dt ≈ 0.500000 Wb/s

Explanation:

Faster flux change (smaller Δt for same ΔΦ) produces larger induced EMF.

3

Step 3: Apply Faraday's Law

Equation:

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

Calculation:

E=−100×0.050.1=−50.000000 V\mathcal{E} = -100 \times \frac{0.05}{0.1} = -50.000000 \text{ V}

Explanation:

Negative sign is Lenz's law: induced EMF opposes the flux change that caused it.

4

Step 4: Report EMF Magnitude

Calculation:

∣E∣=100×0.500000=50.000000 V|\mathcal{E}| = 100 \times 0.500000 = 50.000000 \text{ V}

Result:

∣E∣=50.000000V|ℰ| = 50.000000 V

Explanation:

Magnitude is often quoted for numerical problems; direction comes from Lenz's law and coil orientation.

5

Step 5: Lenz's Law — Direction

Induced current opposes the flux change.

Explanation:

If flux through coil increases, induced current creates field opposing the increase.

6

Step 6: Context

Connect to physical situation.

Explanation:

Same relation powers generators (rotate coil in B), transformers (changing flux in core), and induction cooktops (AC field).

Frequently Asked Questions (FAQ)

What induces EMF?

Any change in flux through the coil: moving magnet, changing current in nearby coil, rotating coil, or changing area.

Generator vs motor?

Generator: mechanical → electrical (induction). Motor: electrical → mechanical (force on current in B).

Why iron core in transformer?

High permeability channels flux, linking primary and secondary efficiently.

Sign of EMF?

Lenz's law gives direction; magnitude from |N ΔΦ/Δt| for uniform change.

Eddy currents?

Induced currents in bulk conductors cause heating — used in induction furnaces, damped in laminations.

Practice MCQs

  1. Faster flux change (same ΔΦ) gives induced EMF that is:
  2. Doubling the number of turns N (same ΔΦ/Δt) doubles:
  3. Lenz's law explains the minus sign in Faraday's law as:
  4. A coil in a constant uniform B field (no motion) has induced EMF:
  5. Motional EMF for rod length l, speed v, field B (mutually perpendicular) is:
  6. SI unit of magnetic flux Φ is:

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