What is magnetic flux and how is it measured?

Magnetic flux Φ is the total magnetic field passing through a surface, measured in webers (Wb) or volt-seconds. It equals the integral of the magnetic field component perpendicular to the surface: Φ = B·A·cos(θ), where B is field strength in teslas, A is area in square meters, and θ is the angle between the field and the surface normal. A field perfectly perpendicular to the loop gives maximum flux; a parallel field gives zero flux.

Why does the induced current oppose the change in flux (Lenz's law)?

Lenz's law is a consequence of energy conservation. If the induced current reinforced the flux change rather than opposing it, you could extract unlimited energy from a simple coil without doing work—violating the first law of thermodynamics. The opposing current creates a force on any moving magnet that resists its motion, requiring you to do mechanical work to maintain the motion. This work is converted to electrical energy in the circuit.

How does Faraday's law explain how a generator works?

An electrical generator rotates a coil in a magnetic field. As the coil turns, the angle between the field and the coil's normal changes continuously, causing the flux to vary sinusoidally: Φ = BA·cos(ωt). Differentiating gives EMF = BAω·sin(ωt)—a sinusoidal alternating voltage. The mechanical rotation energy is converted to electrical energy via the induced EMF. Larger generators use stronger magnets, more coil turns, and higher rotation speeds to maximize EMF.

Home▸Electromagnetism▸Faraday's Law of Induction

🧲 Faraday's Law of Induction

Interactive Faraday law simulation: drag a bar magnet through a coil and watch induced EMF, magnetic flux, and Lenz law current arrows update in real time.

Electromagnetism3DEasy60 FPS⚡ Plasma

About this simulation

This interactive model demonstrates electromagnetic induction by letting you slide a bar magnet along the axis of a solenoid coil. As the magnet moves, the magnetic flux linking the coil changes and an electromotive force appears, computed in real time from Faraday's law, ε = −N dΦ/dt. A scrolling oscilloscope plots the induced EMF while current-direction arrows reveal Lenz's law — the induced current always opposes the change in flux that produced it.

🔬 What it shows

The flux through the coil is modelled with a dipole-like axial profile, Φ(x) = B₀·A / (1 + (x/L)²)^(3/2). Each frame the EMF is found numerically as ε = −N·ΔΦ/Δt, so the waveform, flux bar and current arrows all stay consistent with the magnet's motion and the chosen parameters.

🎮 How to use

Drag the bar magnet through the coil with the mouse or touch, or press the Auto-Oscillate button to drive it sinusoidally. Three sliders set the magnet strength B₀ (0.2–3.0 T), the number of coil turns N (5–200) and the auto frequency (0.1–3.0 Hz). Pause (P) and Reset (R) control the run.

💡 Did you know?

Faraday discovered induction in 1831, but the minus sign — Lenz's law — was stated independently by Heinrich Lenz in 1834. It is a direct expression of energy conservation: the opposing force means you must do mechanical work to generate electrical energy.

Frequently asked questions

What is Faraday's law of induction?

Faraday's law states that a changing magnetic flux through a circuit induces an electromotive force in it. For a coil of N turns the induced EMF equals minus the number of turns times the rate of change of flux, ε = −N dΦ/dt. The faster the flux changes, the larger the induced voltage.

Why does the EMF only appear while the magnet is moving?

Because induction depends on the rate of change of flux, not on flux itself. When the magnet is stationary the flux Φ is constant, dΦ/dt is zero, and so is the EMF. Only motion — or a changing field — produces a non-zero ε, which is why the oscilloscope trace flattens to the zero line whenever the magnet stops.

What do the green and red current arrows mean?

They show the direction of the induced current set by Lenz's law. Green arrows (counter-clockwise) appear when the flux is rising and the coil pushes back against the approaching magnet; red arrows (clockwise) appear when the flux falls and the current reverses to sustain it. The current always opposes the change that created it.

How do the sliders change the result?

Raising the magnet strength B₀ increases the peak flux and therefore the EMF amplitude. Adding coil turns N multiplies the EMF directly, since ε scales with N. In Auto-Oscillate mode the frequency slider sets how quickly the magnet sweeps back and forth, which raises dΦ/dt and the EMF for faster motion.

Is the physics in this simulation accurate?

The relationships are faithful: ε = −N dΦ/dt, Φ = B·A·cosθ, and Lenz's opposing current are all correctly applied. The flux uses a simplified one-dimensional dipole profile along the coil axis rather than a full three-dimensional field integral, so it captures the shape and trends well but the absolute voltage values are illustrative rather than laboratory-exact.

⚙ Under the hood

Drag a bar magnet through a coil of wire and watch the induced EMF ε = −N dΦ/dt in real time. Adjust field strength, coil turns, and motion mode. Demonstrates Lenz's law.

Canvas 2DElectromagnetismFaradayEMFMagnetic FluxLenz's Law

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install