Faraday’s Law of Induction
emf = N · ΔΦ / Δt
Quick answer
This calculator solves emf = −N × ΔΦ / Δt (magnitude N·ΔΦ/Δt) for Induced EMF. With Number of Turns 0.5, Flux Change 10 mWb, Time Interval 20 ms, the result is 0.25 V. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Faraday’s law states that a changing magnetic flux through a coil induces an electromotive force proportional to the number of turns and the rate of change of flux. The minus sign (Lenz’s law) says the induced EMF opposes the change that produced it. This is the principle behind transformers, generators, inductors, induction sensors, and wireless power.
Variables
- emf — Induced electromotive force (V)
- N — Number of turns
- ΔΦ — Change in magnetic flux (Wb)
- Δt — Time over which the change occurs (s)
Practical Notes
Faster flux changes or more turns give higher induced voltage—this is why ignition coils and flyback transformers use many turns and fast current interruption to generate high voltages.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| emf | Induced EMF | V | pV, nV, µV, mV, V, kV |
| N | Number of Turns | — | — |
| dphi | Flux Change | mWb | µWb, mWb, Wb |
| dt | Time Interval | ms | ps, ns, µs, ms, s, min, h |
Step by step
- 1. What you know: Number of Turns 0.5, Flux Change 10 mWb, Time Interval 20 ms
- 2. The relation: emf = −N × ΔΦ / Δt (magnitude N·ΔΦ/Δt)
- 3. Substitute: N = 0.5, dphi = 10 mWb, dt = 20 ms
- 4. Result: Induced EMF = 0.25 V
Worked examples
Minimum range
Given: Number of Turns 0.025, Flux Change 100 µWb, Time Interval 100 µs
Result: Induced EMF = 25 mV
Low range
Given: Number of Turns 0.25, Flux Change 1 mWb, Time Interval 1 ms
Result: Induced EMF = 0.25 V
Typical
Given: Number of Turns 0.5, Flux Change 10 mWb, Time Interval 20 ms
Result: Induced EMF = 0.25 V
High range
Given: Number of Turns 0.8, Flux Change 100 mWb, Time Interval 0.5 s
Result: Induced EMF = 0.16 V
Maximum range
Given: Number of Turns 8, Flux Change 1 Wb, Time Interval 5 s
Result: Induced EMF = 1.6 V
Solving for each variable
Solve for Induced EMF
Number of Turns 0.025, Flux Change 100 µWb, Time Interval 100 µs → 25 mV
Solve for Number of Turns
Induced EMF 0.33 V, Flux Change 100 µWb, Time Interval 100 µs → 0.33
Solve for Flux Change
Induced EMF 0.33 V, Number of Turns 0.025, Time Interval 100 µs → 1.32 mWb
Solve for Time Interval
Induced EMF 0.33 V, Number of Turns 0.025, Flux Change 100 µWb → 7.576 µs
How Induced EMF changes with Number of Turns
| Number of Turns (input) | Induced EMF (result) |
|---|---|
| 0.05 | 25 mV |
| 0.125 | 62.5 mV |
| 0.25 | 125 mV |
| 0.375 | 0.1875 V |
| 0.5 | 0.25 V |
| 0.75 | 0.375 V |
| 1 | 0.5 V |
| 2 | 1 V |
| 3.5 | 1.75 V |
| 5 | 2.5 V |
The same result in other units
| Unit | Value |
|---|---|
| µV | 250000 |
| mV | 250 |
| V | 0.25 |
| kV | 0.00025 |
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<p><a href="https://vbatpower.com/formulas/faraday-law/">Faraday’s Law of Induction</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Faraday’s Law of Induction?
Use emf = −N × ΔΦ / Δt (magnitude N·ΔΦ/Δt). With Number of Turns 0.5, Flux Change 10 mWb, Time Interval 20 ms, Induced EMF works out to 0.25 V.
What is the formula for Faraday’s Law of Induction?
The formula is emf = −N × ΔΦ / Δt (magnitude N·ΔΦ/Δt). Faraday’s law states that a changing magnetic flux through a coil induces an electromotive force proportional to the number of turns and the rate of change of flux.
How do you find Number of Turns when you know the other values?
Rearrange for Number of Turns: with Induced EMF 0.33 V, Flux Change 100 µWb, Time Interval 100 µs, Number of Turns is 0.33.
How do you find Flux Change when you know the other values?
Rearrange for Flux Change: with Induced EMF 0.33 V, Number of Turns 0.025, Time Interval 100 µs, Flux Change is 1.32 mWb.
What units does Faraday’s Law of Induction use?
Induced EMF is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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