# Electromagnetic Induction Simulator - Magnet & Coil, Generator, Rail Rod, Transformer

> Move a magnet through a coil and watch flux, EMF and the galvanometer obey Lenz's law, plus an AC generator, a rod on rails and a transformer.

- URL: https://qilingtools.com/en/math/induction
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Four scenes demonstrate Faraday’s law of induction. In magnet & coil, drag a bar magnet through a coil by hand, let it oscillate, or push it and let it coast. The flux through the coil comes from a closed-form dipole model, and scrolling charts plot the flux linkage NΦ(t) and induced EMF ε(t) as you move. A centre-zero galvanometer swings with the current, arrows on the coil show which way it flows, the coil’s ends are labelled with the induced poles, and a line of text explains the Lenz’s-law push or pull. In coasting mode the eddy braking force is computed from energy conservation, so a lower circuit resistance visibly slows the magnet more. The AC generator spins a coil between magnet poles and reports the peak and RMS EMF of ε = NBAω sin ωt, load power, efficiency and back torque, with a split-ring commutator option for pulsing DC. The sliding rod is pushed along rails by a force (or pulled down by gravity on vertical rails); the motional EMF BLv drives a current whose magnetic force brings it to a terminal velocity, shown with the exact v(t), time constant and power balance. The transformer scene converts voltages, currents and power from the turns ratio, gives the load seen by the primary, and compares line losses with and without stepping up the voltage.

## How to use

1. Pick a scene: magnet & coil, AC generator, sliding rod or transformer
2. Set the magnet strength, turns, coil radius, resistance, rotation rate, field and other values
3. Drag the magnet or press play and watch the galvanometer, the current direction and the flux and EMF charts
4. Read the EMF, current, power, terminal velocity and so on from the results, alongside the formulas

## Features

- Drag, oscillate or launch the magnet, with live Φ(t) and ε(t) charts
- Galvanometer needle, induced-current arrows and induced poles with a Lenz’s-law explanation
- Eddy-current braking on a magnet passing through a closed coil
- AC generator: peak and RMS EMF, power, efficiency and back torque; slip rings or commutator
- Sliding rod: exact v(t), terminal velocity and time constant, with an optional vertical setup
- Transformer ratios, reflected load and a high-voltage transmission loss comparison

## FAQ

### What determines the size of the induced EMF?

Faraday’s law, ε = −N dΦ/dt: what matters is how fast the flux changes, not how large it is. With the magnet sitting in the middle of the coil the flux is at its largest but not changing, so the EMF is zero; it peaks as the magnet passes the ends of the coil, where the flux changes fastest. That’s why, at the same position, moving the magnet faster swings the galvanometer further, and why the EMF chart is largest where the flux chart is steepest.

### How do I find the direction of the induced current with Lenz’s law?

The induced current always sets up a field that opposes the change in flux that caused it. As a north pole approaches the coil, the flux increases and the near end of the coil becomes a north pole that pushes back; as it leaves, the flux decreases and that end becomes a south pole that pulls on it. Once you know which end of the coil is north, the right-hand grip rule gives the direction of the current. The tool labels the induced poles and draws the current arrows for you.

### Why does the rod on the rails reach a terminal velocity?

Moving at speed v the rod has EMF ε = BLv, so the current is I = BLv/R and the magnetic force on it is F = BIL = B²L²v/R, opposing the motion. The faster it goes the bigger the drag, until it equals the applied force F (or mg) and the acceleration drops to zero at v_t = FR/(B²L²). The approach is exponential, v(t) = v_t + (v₀ − v_t)e^(−t/τ) with τ = mR/(B²L²), and at terminal speed all the work done by the force ends up as heat in the resistor.

### Why is electricity transmitted at high voltage?

To deliver power P at voltage U the line carries a current I = P/U, and the heating loss in the line is P_loss = I²r = (P/U)²r. Raising the voltage by a factor k cuts the current to 1/k and the loss to 1/k²: going from 400 V to 10 kV leaves just 1/625 of the loss. A transformer changes AC voltage and current while ideally keeping the power the same, U₁/U₂ = N₁/N₂ and I₁/I₂ = N₂/N₁. The transmission comparison in the tool lets you try this directly.

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