Calculator
Use direct magnetic flux values or compute flux from magnetic field, area, and angle. Choose what to solve, then submit.
Formula used
Magnetic flux: Φ = B × A × cos(θ)
Flux change: ΔΦ = Φ₂ − Φ₁
Average flux change rate: dΦ/dt = ΔΦ ÷ Δt
Faraday’s law: ε = −N × (dΦ/dt)
Turns from target emf: N = |ε| ÷ |dΦ/dt|
Current and power: I = |ε| ÷ R, P = |ε| × I
The negative sign comes from Lenz’s law. It shows the induced emf opposes the change in magnetic flux. In practical design work, engineers often compare emf magnitude, but the sign still matters when discussing direction.
How to use this calculator
- Select whether you want induced emf, required turns, or required flux rate.
- Choose a flux input method. Use direct flux values or calculate flux from field, area, and angle.
- Enter the time interval for the flux change.
- Provide turns when solving for emf or required flux rate.
- Provide desired emf when solving for turns or required flux rate.
- Optionally enter resistance to estimate current and power.
- Press Calculate to show results above the form and below the header.
- Use the export buttons to save results as CSV or PDF.
Example data table
| Case | Φ₁ (Wb) | Φ₂ (Wb) | Δt (s) | N | |ε| (V) |
|---|---|---|---|---|---|
| Laboratory induction coil | 0.02 | 0.08 | 0.50 | 250 | 30.00 |
| Fast flux reversal | 0.06 | -0.02 | 0.20 | 180 | 72.00 |
| Low-turn sensor coil | 0.01 | 0.03 | 1.00 | 60 | 1.20 |
| Generator winding test | -0.04 | 0.05 | 0.15 | 320 | 192.00 |
FAQs
1. What does this Faraday’s law calculator compute?
It computes induced emf from magnetic flux change. It can also estimate required coil turns or required flux rate. When resistance is added, it reports current and electrical power.
2. Why can the induced emf be negative?
The negative sign represents Lenz’s law. It shows the induced voltage opposes the flux change causing it. Magnitude is useful for sizing, while sign explains direction.
3. When should I use direct flux inputs?
Use direct flux values when magnetic flux is already measured or known from another calculation. It is quicker and reduces unnecessary inputs.
4. When should I use field, area, and angle inputs?
Use field-based inputs when flux is not directly available. The calculator finds flux from magnetic field strength, coil area, and orientation angle.
5. What units should I enter?
Enter magnetic flux in webers, magnetic field in tesla, area in square meters, time in seconds, resistance in ohms, and voltage in volts.
6. Does the calculator use average or instantaneous emf?
This version uses the average flux change over the entered time interval. For instantaneous emf, you would need a continuously changing flux function.
7. Can this help with generator or sensor design?
Yes. It is useful for estimating winding requirements, expected voltage, and how changing field strength, area, or timing affects electromagnetic output.
8. Why does resistance appear optional?
Resistance is only needed to estimate current and power. Faraday’s law itself depends on flux change rate and coil turns, not resistance.