Faraday's law calculator
Choose a coil with a changing field or a conductor moving through a field. Enter the turns, the field before and after, the coil area and the time, or the field, length and speed of the rod. Add the circuit resistance to see the current and the power it delivers.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
Coil
- Enter the number of turns and the coil area.
- Enter the field before and after the change (in tesla) and how long the change takes.
- Enter the resistance of the circuit to see the current and the power.
Moving conductor
- Enter the field, the length of the conductor inside it and its speed.
- Enter the resistance of the circuit to see the current, the power and the braking force.
- Flux: Φ = B × A; ΔΦ = (B₂ − B₁) × A.
- Coil EMF: |ε| = N × |ΔΦ| ÷ Δt.
- Motional EMF: ε = B × L × v.
- Current and power: I = ε ÷ R, P = ε² ÷ R; braking force F = B × I × L.
Worked example
A 100-turn coil of 50 cm² (0.005 m²) sees the field rise from 0 to 0.5 T in 0.1 s. ΔΦ = 0.5 × 0.005 = 0.0025 Wb and ε = 100 × 0.0025 ÷ 0.1 = 2.5 V. With 2 Ω in the circuit, the current is 1.25 A and the power 3.125 W.
A 0.2 m rod slides at 5 m/s across 0.5 T: ε = 0.5 × 0.2 × 5 = 0.5 V. Through 2 Ω the current is 0.25 A, the power 0.125 W and the force holding it back 0.5 × 0.25 × 0.2 = 0.025 N.
Tips
- Average, not instantaneous. ΔΦ ÷ Δt gives the average EMF over the change; a sudden change gives a high peak.
- Faster change, higher voltage. Halving Δt doubles the EMF for the same flux change.
- Earth’s field is small. About 50 µT (0.00005 T), so a 1.5 m car axle at 25 m/s induces only 0.001875 V.
Frequently asked questions
What does Faraday's law say?
A changing magnetic flux through a circuit induces an EMF equal to the rate of change of the flux, ε = −N × ΔΦ ÷ Δt for a coil of N turns. The flux through one turn is Φ = B × A when the field is perpendicular to the coil.
What does the minus sign mean?
It is Lenz's law, the induced current flows so as to oppose the change that caused it. The calculator shows the size of the EMF and the signed flux change; the minus sign tells the direction, not the magnitude.
What is motional EMF?
A conductor of length L moving at speed v across a field B has an EMF ε = B × L × v between its ends. With a closed circuit a current flows, and the field pushes back on it with F = B × I × L, which is why a generator gets harder to turn under load.
Does the field have to be perpendicular?
The formulas here assume it is. If the field makes an angle θ with the normal of the coil, multiply the flux by cos θ; for a rod, use the part of the velocity across the field.