Induced EMF Calculator
Calculate induced electromotive force using Faraday's law or motional EMF. Every answer includes SI conversions, step-by-step formula substitution, and a labelled magnetic-flux diagram.
Induced EMF Diagram and Values
The visual labels connect changing magnetic field, coil motion, and the voltage produced.
Step-by-Step Solution
Here's exactly how this answer was calculated, one step at a time.
Given: N = 100, ΔΦ = 5 mWb, Δt = 0.2 s
Step 1: Convert values to SI units
ΔΦ = 5 mWb = 0.005 WbStep 2: Write the induced EMF formula
Faraday's law connects induced voltage to the rate magnetic flux changes through each turn.
|ε| = N|ΔΦ| / ΔtStep 3: Substitute known values
ε = 100 × 0.005 / 0.2Step 4: Calculate induced voltage
|ε| = 2.5 V
The induced EMF magnitude is:
2.5 V
Free Induced EMF Calculator
This Induced EMF Calculator calculates the voltage generated when magnetic flux changes through a coil or when a conductor moves through a magnetic field. Choose Faraday's law for changing flux or the motional EMF formula, enter the values, and get a clear answer in volts and millivolts. The solution section converts all units, substitutes values into the formula and shows the arithmetic. The diagram displays the coil, magnetic field, change or motion, and the exact result together.
Use it for physics questions on generators, coils, transformers, rail conductors and electromagnetic induction. The displayed EMF is a magnitude. Lenz's law determines the polarity and current direction: the induced effect always opposes the change that created it.
Faraday's Law of Electromagnetic Induction
Faraday's law gives the magnitude of induced EMF as |ε| = N|ΔΦ|/Δt. Epsilon is induced electromotive force in volts, N is the number of turns, ΔΦ is magnetic flux change in webers, and Δt is time in seconds. The signed form is ε = −NΔΦ/Δt; the minus sign represents Lenz's law.
Magnetic flux measures field passing through a surface. For a uniform field, Φ = BA cos θ, where A is area and θ is angle between field and area normal. Flux can change by changing B, area, orientation, or by moving a coil into or out of the field.
Faraday's Law Worked Example
A 100-turn coil experiences a flux change of 5 mWb in 0.20 seconds. Convert 5 mWb to 0.005 Wb. Then |ε| = 100 × 0.005 / 0.20 = 2.5 V. Doubling turns or flux change doubles the induced EMF; halving the time also doubles it.
The worked answer is an ideal open-circuit EMF. If the coil is connected to a resistor, current depends on total resistance through I = V/R. A real coil also has resistance and inductance, so a practical generator may differ from this simple result.
Motional EMF Formula
A straight conductor of length ℓ moving at speed v across a magnetic field has motional EMF |ε| = Bℓv sin θ. Use B in tesla, length in metres and speed in metres per second. The angle is between motion and the magnetic field; force is strongest at 90 degrees and zero for motion parallel to the field.
For B = 50 mT, ℓ = 0.30 m, v = 10 m/s and θ = 90°, convert field to 0.050 T. The result is ε = 0.050 × 0.30 × 10 × 1 = 0.15 V. This principle is used in generators, velocity sensors and moving-conductor demonstrations.
Lenz's Law and Direction
Lenz's law says induced current creates a magnetic field opposing the original change in flux. If flux into a coil increases, the coil produces a field out of the page to resist the increase. Apply the right-hand rule to find the needed induced field, then determine the required current direction.
This opposition does not violate energy conservation. Mechanical work is required to move a conductor against the induced magnetic effect, and that work becomes electrical energy and often heat in the circuit.
Units, Applications and Design Notes
One weber equals one tesla square metre. Prefixes matter: 1 mWb = 0.001 Wb and 1 mT = 0.001 T. Keep the time in seconds. Common applications include AC generators, transformers, wireless chargers, induction cooktops, bicycle dynamos and metal detectors.
For real designs consider coil resistance, core material, saturation, waveform, load, frequency, fringe field and insulation rating. Never use a simplified online calculation as a high-voltage or high-current safety design. Follow component specifications and appropriate electrical standards.
Frequently Asked Questions
What is the induced EMF formula?
Faraday's law is ε = −NΔΦ/Δt. The calculator reports magnitude N|ΔΦ|/Δt.
What does the negative sign in Faraday's law mean?
It represents Lenz's law: the induced EMF opposes the change in magnetic flux.
What is the motional EMF formula?
For a moving straight conductor, ε = Bℓv sin θ.
What unit is induced EMF measured in?
Induced EMF is measured in volts (V), often millivolts for small values.
How can I increase induced voltage?
Increase turns, magnetic field, coil area or speed of flux change; decrease the time over which flux changes.
Why is no EMF induced with no flux change?
Faraday's law depends on the rate of change of flux. A steady flux produces zero induced EMF.
Does induced EMF always produce current?
EMF can exist in an open circuit, but a sustained current requires a closed conducting path.