Electromagnetic Induction Simulator
Equations in this simulation
| ε | induced EMF | the voltage the changing flux drives round the coil; the minus sign is Lenz's law: the current it drives opposes the change | |
|---|---|---|---|
| N | Turns on the coil N (or on the primary) | each turn adds the same EMF | |
| Φ | magnetic flux through one turn | in webers; the chart shows how ε depends on where the magnet is |
With the current values:
| m | Magnet strength m (A·m²) | the magnet's dipole moment; a 1 cm³ neodymium magnet is about 1 A·m² | |
|---|---|---|---|
| a | radius of the coil | 2 cm | |
| d | distance from the magnet's center to the turn | the magnet is treated as a point dipole, which is rough when it is inside the coil |
With the current values:
| R | Load resistance R (ohms) | the coil's own wire adds 0.02 Ω per turn |
|---|
With the current values:
| B | Field B (tesla, generator) | uniform between the poles | |
|---|---|---|---|
| A | Coil area A (cm², generator) | the flux through the coil is N B A cos ωt | |
| ω | angular speed, 2πf | from Frequency f (Hz, generator and transformer) |
With the current values:
| V_p, V_s | primary and secondary voltage | an ideal transformer: no losses, all the flux links both coils | |
|---|---|---|---|
| N_s | Turns on the secondary N_s (transformer) | more turns than the primary steps the voltage up and the current down |
With the current values:
How to use the electromagnetic induction simulator
- With A magnet and a coil, the magnet moves in and out of the coil on its own, passes right through, or follows the position slider when you choose By hand. The galvanometer swings one way as the magnet goes in and the other way as it comes out, and stays at zero while the magnet is still: only a changing flux makes a current. The letters over the coil show its induced poles, always pushing back against the change (Lenz's law).
- Change the speed, the magnet's strength and the number of turns, and watch the EMF scale with each, as Faraday's law says. Turn the magnet round to reverse the current. The chart shows the EMF the magnet makes at every position for the speed you set: a peak going in, an opposite peak coming out, and zero at the center.
- Switch to the generator to spin a coil in a uniform field and see a sine wave come out, with its peak and RMS values, or to the transformer to step a voltage up or down with the turns ratio. Tick direct current to see the transformer give nothing at all. The Ohm's Law Calculator works out the current in the load.
Frequently asked questions
What is Faraday's law of induction?
A changing magnetic flux through a coil induces an EMF equal to the number of turns times the rate of change of the flux: ε = −N dΦ ÷ dt. Moving the magnet faster, using a stronger magnet or adding turns all increase the voltage. A magnet that sits still inside the coil induces nothing.
What does Lenz's law mean?
The induced current flows in the direction that opposes the change that caused it; that is the minus sign in Faraday's law. A magnet pushed in meets a coil whose near end becomes the same pole and repels it; a magnet pulled out is attracted back. You have to do work against this force, which is where the electrical energy comes from.
How does a generator make alternating current?
A coil spinning in a magnetic field has a flux N B A cos ωt through it, which changes all the time, so it produces an EMF N B A ω sin ωt. The voltage reverses twice every turn. Power stations spin their generators 50 or 60 times a second, which sets the mains frequency.
Why does a transformer not work on direct current?
A transformer works because the alternating current in the primary makes a changing flux in the core, which induces a voltage in the secondary. Steady direct current makes a steady flux, so after the moment it is switched on there is no change and no output. Worse, the primary is then limited only by its wire's resistance and can overheat.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.