Induced Voltage Calculator: Faraday’s Law Explained

An induced voltage calculator estimates the electromotive force produced when magnetic flux through a coil changes. Enter the magnetic field, coil area, change time, and number of turns to calculate the average induced voltage in volts.

Formula

For a uniform magnetic field perpendicular to a flat coil, the average induced voltage magnitude is calculated from Faraday’s law:

V = N × A × ΔB ÷ Δt

• V is the average induced voltage, in volts (V).
• N is the number of turns in the coil, a count with no unit.
• A is the coil area, in square metres (m²).
• ΔB is the change in magnetic field, in teslas (T).
• Δt is the time over which the field changes, in seconds (s).

The calculator uses the magnitude of the field change and assumes the field is perpendicular to the coil. More generally, magnetic flux is Φ = B A cos(θ), and Faraday’s law is ε = −N × ΔΦ/Δt. Here Φ is magnetic flux in webers (Wb), θ is the angle between the field and the coil’s area direction, and the minus sign expresses Lenz’s law: the induced effect opposes the change in flux. The calculator’s result is a positive average magnitude, not a signed voltage waveform.

Worked Example

Using the calculator’s default values: magnetic field change ΔB = 0.5 T, area A = 0.01 m², turns N = 100, and change time Δt = 0.1 s.

1. Calculate the field change through one turn: A × ΔB = 0.01 × 0.5 = 0.005 Wb.
2. Multiply by the number of turns: 100 × 0.005 = 0.5 Wb-turn.
3. Divide by elapsed time: 0.5 ÷ 0.1 = 5 V.

The average induced voltage magnitude is 5.000 V. The actual voltage polarity depends on the direction of the field change and how the coil terminals are oriented.

What Induced Voltage Means

Induced voltage is the potential difference created when magnetic flux linked with a conductor changes. A changing field can induce voltage in a stationary coil; alternatively, motion can change the field passing through a coil. In a generator, rotation changes flux through windings. In a transformer, alternating current in one winding creates a changing magnetic field that induces voltage in another winding.

The key quantity is changing flux, not simply the presence of a magnetic field. A strong but steady field through a stationary coil produces no continuing induced voltage under the idealized model. A weaker field that changes rapidly can produce a larger voltage. Increasing the number of turns or the coil area also increases the result when the other values and orientation are held constant.

When to Use This Calculator

This calculator is useful for a first estimate when the field is approximately uniform, the coil is flat, and the field direction is perpendicular to its area. It can help explain basic induction experiments or compare how changing turns, area, field change, or elapsed time affects average voltage.

• Use teslas for magnetic field change, not gauss, without conversion. One tesla equals 10,000 gauss.
• Use square metres for area. Convert square centimetres by dividing by 10,000; for example, 100 cm² = 0.01 m².
• Use seconds for elapsed time. If the change takes milliseconds, convert them to seconds: 10 ms = 0.010 s.
• Enter the number of turns as a count. A coil with 250 turns uses N = 250.

For comparison across common unit systems, 1 V = 1,000 millivolts, and 1 square inch is 0.00064516 m². Convert all inputs before applying the formula; mixing inches, square metres, milliseconds, or gauss directly will give a misleading answer.

Assumptions and Limitations

The simple expression N A ΔB/Δt assumes the field is uniform over the coil, the coil area and orientation remain fixed, and the field changes at a constant rate or that an average over the stated interval is acceptable. If the field varies irregularly, the calculation gives average induced voltage over the whole interval, not the instantaneous voltage at every moment.

For a coil at an angle, include the changing flux component: Φ = B A cos(θ). If the field is nonuniform, divide the area into regions or use a flux integral. If the coil moves or rotates, its area direction may change too, so calculate the change in flux rather than only the change in magnetic field. For alternating fields, voltage changes over time; a peak value, RMS value, or waveform may be needed depending on the question.

Real circuits can also be affected by resistance, inductance, capacitance, geometry, and measurement equipment. Those effects do not alter Faraday’s law, but they can make the voltage measured at a particular point differ from a basic average estimate. This calculator does not determine current or power; those require additional circuit information.

Common Mistakes

• Using the field itself instead of its change: ΔB is the difference between final and initial field values. A constant field has ΔB = 0 in this fixed-coil model.
• Confusing area with dimensions: multiply the coil’s side lengths to get area, then convert to m². Do not enter a length as the area.
• Ignoring orientation: the full field contributes only when perpendicular to the coil plane. At other angles, use the flux component B cos(θ).
• Using the wrong time interval: a shorter change time produces a larger average voltage for the same flux change. Confirm whether the interval is in seconds or milliseconds.
• Treating the answer as a guaranteed terminal reading: the result is an ideal average induced EMF magnitude, not necessarily the voltage under a connected load.

Frequently Asked Questions

What is the formula for induced voltage?
Faraday’s law is ε = −N × ΔΦ/Δt. For a uniform perpendicular field and fixed coil area, its magnitude simplifies to V = N × A × ΔB/Δt.

Can a stationary coil have induced voltage?
Yes. The coil can remain still while the magnetic field through it changes. What matters is changing magnetic flux, not motion alone.

Does a stronger magnet always create more induced voltage?
No. A stronger field can increase voltage if the flux changes, but a steady field through a stationary coil does not produce continuing induced voltage in this model. The rate of flux change matters.

How do I calculate induced voltage when the coil is angled?
Calculate magnetic flux using Φ = B A cos(θ), then apply ε = −N × ΔΦ/Δt. Compare the initial and final flux, including any change in angle.

Is induced voltage the same as current?
No. Voltage is the induced electromotive force. The current that flows depends on the circuit’s impedance and connection; voltage alone is not enough to calculate it.

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in b | Magnetic field change | T | 0.5 | 0
in a | Coil area | m² | 0.01 | 0
in n | Number of turns | turns | 100 | 0
in t | Change time | s | 0.1 | 0
out v | Average induced voltage | V | n * a * b / t | 3
out emf | Magnitude of induced EMF | V | v | 3