Electromagnetic Induction Simulator
Move a bar magnet through a coil and see the induced EMF. Observe Faraday's and Lenz's laws as flux changes.
Electromagnetic Induction
Faraday's law states that the induced EMF in a coil equals the negative rate of change of magnetic flux through the coil: ε = -N dΦ/dt. The negative sign reflects Lenz's law: the induced current opposes the change causing it.
Magnetic Flux
Magnetic flux Φ = B·A·cos(θ) measures how much magnetic field passes through a surface area A. When a bar magnet approaches a coil, the flux through the coil increases, inducing an EMF that opposes that increase.
Key Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| N | Turns | — | Number of loops in the coil |
| Φ | Magnetic flux | Wb | B·A through the coil — depends on magnet distance |
| ε | Induced EMF | V | ε = -N dΦ/dt by Faraday's law |
| x | Magnet position | m | Distance of magnet from coil center |
| v_s | Oscillation speed | Hz | Frequency of magnet back-and-forth motion |
| B₀ | Magnet strength | — | Relative field strength of the bar magnet |
Lenz's Law Direction
When the north pole approaches, flux increases through the coil. The induced current creates a magnetic field opposing this increase — the coil face facing the magnet acts as a north pole, repelling the magnet. When the magnet recedes, the coil 'attracts' the receding magnet (south pole faces magnet).
Key Formulas
| Formula | Description | Notes |
|---|---|---|
| ε = -N dΦ/dt | Faraday's law | Negative sign = Lenz's law (opposition) |
| Φ = B·A·cos θ | Magnetic flux | θ = 0 for field perpendicular to coil face |
| ε ∝ N | More turns → larger EMF | Each turn adds its contribution independently |
| ε ∝ dΦ/dt | Faster change → larger EMF | Moving magnet faster gives larger EMF |
Frequently Asked Questions
Why does moving a magnet faster induce a larger EMF?
A faster magnet changes the flux more rapidly (larger dΦ/dt), giving a larger EMF by Faraday's law ε = -N dΦ/dt.
What determines the direction of induced current?
Lenz's law: the induced current creates a magnetic field that opposes the change in flux. Moving a north pole toward a coil induces a current that creates a repulsive north pole facing the magnet.
Why does more turns in the coil increase the EMF?
Each turn of the coil contributes its own EMF. Since all turns experience the same changing flux, the total EMF is N times the EMF per turn: ε_total = -N dΦ/dt.
Is energy conserved in electromagnetic induction?
Yes. Lenz's law ensures energy conservation. The mechanical energy used to push the magnet against the opposing magnetic force is converted to electrical energy in the coil circuit, which then dissipates as heat in any resistance.