Library / Foundations: Physics / FPH-29
Foundations: Physics
Induced emf (Faraday’s law)
Average emf in a coil when its flux linkage changes.
- Ref
- FPH-29
- Rev
- v1
- Field
- Foundations: Physics
- Result
- ℰ [V]
For a uniform field, θ is measured to the area normal. N is the number of identical turns. The induced emf opposes the change in flux linkage. The calculator gives the average emf when the flux falls to zero in time Δt.
A changing magnetic flux through a coil produces a voltage; faster change or more turns gives more.
Calculator
- Flux Φ125 µWb
- Flux linkage NΦ25,000 µWb
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Turning a coil or changing a field quickly gives a bigger emf, which is how generators and microphones work.
- The minus sign shows the induced current opposes the change that caused it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| B Field | 0.1 to 2,000 mT | 0.0025 | 50 | 50 | +10% | +10 % |
| N Turns | 1 to 5,000 | 0.00625 | 31.25 | 31.24 | +10% | +10 % |
| Δt Time of change | 1 to 1,000 ms | 0.025 | 25 | 24.98 | +10% | −9.09 % |
| A Coil area | 1 to 500 cm² | 0.05 | 25 | 24.95 | +10% | +10 % |
| θ Angle to the normal | 0 to 75 ° | 0.3235 | 1.25 | 0.9265 | +10% | 0 % |
Sweep of Time of change
| Time of change (ms) | Average emf (V) |
|---|---|
| 1 | 25 |
| 2.371 | 10.54 |
| 5.623 | 4.446 |
| 13.34 | 1.875 |
| 31.62 | 0.7906 |
| 74.99 | 0.3334 |
| 177.8 | 0.1406 |
| 421.7 | 0.05928 |
| 1,000 | 0.025 |
Sweep one variable
Variables and how each one contributes
Average emf
What the equation gives you. Everything else feeds it.
Turns
Number of turns. Directly proportional.
Field
Magnetic flux density. Directly proportional.
Coil area
Area of one turn. Directly proportional.
Angle to the normal
Angle between the field and the coil normal. Reduces the flux by cos θ.
Time of change
Time over which the flux changes. Inversely proportional.
Worked example with the values above
- Flux: Φ = BA cos θ = 0.05 × 0.0025 × 1 = 1.25×10−4 Wb.
- Rate of change: ΔΦ/Δt = 1.25×10−4 / 0.02 s.
- emf = N ΔΦ/Δt = 1.25 V.
Assumptions and limits
- Uniform field over the coil.
- Flux changes at a roughly steady rate.
Common mistakes
- Using the angle to the plane instead of the normal.
- Forgetting the number of turns.
Statistics and uncertainty
Timing of rapid changes is the main uncertainty; the emf is inversely proportional to Δt.
Where it is used
- Generators, sensors and pick-ups.
- Eddy-current and induction effects.
Maths you need
- Magnetic flux: BA cos θ
- Rates of change: flux per second