⚡ Faraday's Law Calculator
Calculate induced EMF from magnetic flux change
Number of loops in the coil
Change in magnetic flux through the loop. Use positive value (magnitude)
Time interval over which flux changes
How to Use This Calculator
Enter Number of Turns
Input the number of loops (turns) in the coil or wire loop. For a single loop, enter 1. For multiple loops in series, enter the total number of turns.
Enter Change in Magnetic Flux
Input the change in magnetic flux in Weber (Wb). This is the difference between final and initial magnetic flux: ΔΦ = Φ_final - Φ_initial. You can enter the magnitude (positive value).
Enter Time Change
Input the time interval over which the magnetic flux changes, in seconds. This is Δt = t_final - t_initial.
Calculate
Click the "Calculate Induced EMF" button to get the magnitude of induced EMF in Volts. The negative sign in Faraday's law indicates the direction opposes the change (Lenz's law).
Formula
EMF = -N × (ΔΦ / Δt)
Where:
- EMF = Induced Electromotive Force (Volts, V)
- N = Number of Turns (loops in the coil)
- ΔΦ = Change in Magnetic Flux (Weber, Wb)
- Δt = Change in Time (seconds, s)
Magnetic Flux:
Φ = B × A × cos(θ), where B is magnetic field, A is area, and θ is angle
Example Calculation:
For a 100-turn coil with flux change of 0.01 Wb in 0.1 seconds:
|EMF| = 100 × 0.01 / 0.1
|EMF| = 10 V
Note: The negative sign indicates that the induced EMF creates a current whose magnetic field opposes the change in flux (Lenz's law). The magnitude is what we calculate here.
About Faraday's Law Calculator
The Faraday's Law Calculator determines the induced electromotive force (EMF) in a coil or loop when the magnetic flux through it changes. Faraday's law is fundamental to understanding electromagnetic induction, which is the basis for generators, transformers, and many electrical devices. The induced EMF creates a current that opposes the change in flux (Lenz's law).
When to Use This Calculator
- Generator Design: Calculate induced EMF in generators and alternators
- Transformer Analysis: Understand voltage induction in transformer windings
- Induction Motors: Analyze EMF generation in motor windings
- Physics Education: Solve problems involving electromagnetic induction
- Circuit Design: Understand back EMF in inductive circuits
Why Use Our Calculator?
- ✅ Quick Calculation: Instantly determine induced EMF from flux change
- ✅ Multiple Turns: Accounts for coils with multiple loops
- ✅ Educational Tool: Learn about electromagnetic induction and Lenz's law
- ✅ Free Tool: No registration or payment required
- ✅ Practical Applications: Essential for understanding generators and transformers
Common Applications
Electrical Generators: Calculate the EMF generated when a coil rotates in a magnetic field or when a magnet moves near a coil. This is the fundamental principle behind power generation in hydroelectric, wind, and steam turbines, where mechanical energy is converted to electrical energy through electromagnetic induction.
Transformers: Understand how changing magnetic flux in the primary coil induces voltage in the secondary coil. The induced EMF depends on the number of turns and the rate of flux change, allowing transformers to step up or step down voltages for power transmission and distribution.
Inductive Sensors: Analyze EMF generation in sensors that detect motion, position, or proximity by measuring changes in magnetic flux. Applications include speed sensors, position encoders, and metal detectors that rely on induced currents from changing magnetic fields.
Tips for Best Results
- Faster flux change (smaller Δt) produces larger induced EMF
- More turns (larger N) increases induced EMF proportionally
- The negative sign indicates Lenz's law - induced current opposes the change
- Magnetic flux Φ = B × A × cos(θ) where B is field, A is area, θ is angle
- For constant flux change rate, EMF is constant; for varying rate, use calculus
Frequently Asked Questions
What is Faraday's Law?
Faraday's law states that a changing magnetic flux through a loop induces an electromotive force (EMF) in the loop. The magnitude is proportional to the number of turns and the rate of flux change: EMF = -N(ΔΦ/Δt). The negative sign indicates Lenz's law.
What is Lenz's Law?
Lenz's law states that the induced current creates a magnetic field that opposes the change in magnetic flux that produced it. This is represented by the negative sign in Faraday's law and ensures conservation of energy - work must be done to change the flux.
How do I calculate magnetic flux?
Magnetic flux Φ = B × A × cos(θ), where B is magnetic field strength (Tesla), A is the area of the loop (m²), and θ is the angle between the magnetic field and the normal to the loop. For perpendicular fields, cos(90°) = 0, so flux is zero.
What's the difference between EMF and voltage?
EMF (electromotive force) is the potential difference created by a source (like a changing magnetic field), while voltage is the potential difference across a component. In a generator, EMF is generated, which becomes voltage when current flows through a load.
Why does the number of turns matter?
Each turn contributes to the total induced EMF. For N turns in series, the EMF is N times larger because each turn experiences the same flux change and their EMFs add together. This is why generator coils and transformer windings use many turns.
What if flux change isn't constant?
For non-uniform flux changes, use calculus: EMF = -N dΦ/dt. For sinusoidal changes (AC generators), the instantaneous EMF varies with time: EMF(t) = -N d(BAcos(ωt))/dt = NBAωsin(ωt), where ω is angular frequency.