The interactive animation shows how electric current is generated by motion. In the upper left area of the animation, a 3D scene is displayed, consisting of a horseshoe magnet and a metal cylinder (conductor).
The conductor can be moved interactively through a magnetic field. In this case, the law of induction describes the formation of an electric field inside the conductor. Inside the metal cylinder, blue spheres represent the electric current.
Instructions for Use
The windows can be enlarged or reduced by clicking on them, just like with all animations.
After starting the application, you can view the animation in full screen mode. To do this, click on “View” and then on “Full Screen”:
To exit full screen mode, press the Esc key.
Description of the Animation
The animation shows a 3D model with a horseshoe magnet in the upper left window. Inside the magnetic field is a cylindrical conductor. The electrons are represented by blue spheres.
The magnetic field of the horseshoe magnet can be shown or hidden as needed.
In the upper right window, the objects are shown in a profile view. In this view, the conductor can be moved with the mouse.
The law of induction tells us that electrons begin to move when the conductor is displaced at right angles to the magnetic field lines.
\[ U_\text{ind} = – \frac{\Delta \Phi}{\Delta t} \]
- U_ind: induced voltage
- ΔΦ: change in magnetic flux
- Δt: time interval
The law of induction can also be written in a form that more directly describes a conductor moving through a magnetic field:
\[ U_\text{ind} = -B \cdot v \cdot l \cdot \sin(\alpha) \]
- U_ind: induced voltage
- B: magnetic flux density
- v: velocity of conductor
- l: length of conductor in magnetic field
- α: angle between direction of motion and field lines
This shows that the induced voltage is proportional to the speed at which the conductor moves.
The relationship between induced voltage and speed is clearly shown in the graph in the lower-right window.
The magnetic field lines can also be shown in the animation.
Ampère’s circuital law states that a circular magnetic field forms around a current-carrying conductor.
\[ B = \frac{\mu_0 \cdot I}{2 \pi \cdot r} \]
- B: magnetic flux density
- μ₀: magnetic field constant
- I: current
- r: distance from conductor
Note: μ₀ is the magnetic field constant. In the profile view, the resulting magnetic field can also be displayed.
The resulting magnetic field is the superposition of the dynamic field around the conductor and the static field of the horseshoe magnet.
The Lorentz force law describes the force acting on the current-carrying conductor in the magnetic field.
\[ \vec{F} = q \cdot (\vec{v} \times \vec{B}) \]
- F: Lorentz force
- q: charge
- v: velocity
- B: magnetic flux density
This force opposes the conductor’s motion. Moving the conductor therefore requires not just displacement but also effort – in other words, mechanical work is done.
In technical applications this work is typically provided by a turbine, which may be driven by steam or – in the case of a wind turbine – by wind.
Note: The animation takes into account the difference between technical and physical current direction. Electrons are represented by blue spheres and indicate the physical current direction. The dot and cross symbols refer to the technical current direction.
In our everyday lives, electromagnetic induction operates almost everywhere in the background: In power plants, generators produce electricity by moving conductors through magnetic fields; bicycle dynamos convert the rotation of the wheel into electrical energy; induction cooktops heat pots because eddy currents form in the metal; transformers in chargers adjust voltages so that devices can be operated safely; wireless chargers for smartphones transfer energy through changing magnetic fields.
What Happens Physically When You Move the Conductor?
The process of electromagnetic induction can be understood step by step:
Step 1 — Initial situation: The cylindrical conductor rests between the poles of the horseshoe magnet. The free electrons in the metal move randomly (thermal motion), but there is no directed movement — no current flows and no voltage is present.
Step 2 — Motion begins: As soon as the conductor is displaced perpendicular to the field lines, the electrons move through the magnetic field together with the conductor. Each electron now experiences the Lorentz force, which acts perpendicular to both the direction of motion and the magnetic field.
Step 3 — Charge separation: The Lorentz force pushes the electrons toward one end of the conductor. This creates an excess of electrons (negative) at one end and a deficit (positive) at the other. This charge separation produces an electric voltage — the induced voltage.
Step 4 — Measurable voltage: The induced voltage is proportional to the speed of the movement, the strength of the magnetic field, and the length of the conductor within the field. This is precisely the relationship described by the formula Uind = −B · v · l · sin(α).
Step 5 — Current flow in a closed circuit: If the conductor is connected to a closed circuit, the induced voltage drives an electric current. This current in turn generates its own magnetic field around the conductor (Ampère’s circuital law) and creates a force that opposes the motion (Lenz’s law).
A Brief History — Faraday’s Discovery
Electromagnetic induction was discovered in 1831 by the English physicist Michael Faraday. Faraday was not a formally trained scientist — he began his career as a bookbinder’s apprentice and was largely self-taught in the natural sciences.
His decisive experiment was surprisingly simple: he wound two wire coils around an iron ring and observed that when the current in one coil was switched on or off, a brief current appeared in the other coil — even though the two coils were not directly connected. Faraday had demonstrated that a changing magnetic field can produce an electric voltage.
Independently, the American physicist Joseph Henry made the same discovery at almost the same time. However, Faraday published his results first and formulated the law of induction that now bears his name.
This discovery was one of the most consequential in the history of physics: without it, there would be no generators, no transformers, and no electrical power supply as we know it today.
Everyday Applications in Detail
Electromagnetic induction is present in everyday life more often than most people realize. Two particularly illustrative examples:
The Bicycle Dynamo
A bicycle dynamo works on exactly the principle shown in the animation. Inside, a small permanent magnet rotates, driven by the tire. A stationary wire coil surrounds this magnet. As the magnet rotates, the magnetic flux through the coil changes continuously — and according to the law of induction, this produces an alternating voltage that powers the bicycle light. The faster you ride, the brighter the light shines — because a higher rotational speed means a faster change in flux and thus a higher induced voltage.
The Induction Cooktop
An induction cooktop generates a rapidly alternating magnetic field beneath the glass-ceramic surface using a coil. This alternating magnetic field penetrates the bottom of the cooking pot and induces eddy currents — circularly flowing electric currents in the metal. These eddy currents generate heat directly in the pot’s base through the electrical resistance of the material. This is why induction cooktops only work with ferromagnetic pots (e.g., steel or cast iron) — aluminum or copper pots are not heated sufficiently because strong eddy currents cannot form in them.
Lenz’s Law — The Meaning of the Minus Sign
In the formula for the law of induction, the minus sign stands out:
\[ U_\text{ind} = – \frac{\Delta \Phi}{\Delta t} \]
This minus sign is not a mathematical detail — it expresses a fundamental physical principle: Lenz’s law, named after the German-Baltic physicist Heinrich Lenz (1834).
Lenz’s law states: The induced voltage is always directed such that the current it causes opposes the cause of the induction.
In practical terms: when the conductor in the animation is moved to the right, the induced current flows in such a direction that its magnetic field opposes the rightward motion. The conductor, so to speak, “resists” being displaced. This is why force must be applied to move it — and it is precisely this mechanical work that is converted into electrical energy.
Lenz’s law is a direct consequence of the conservation of energy: if the induced current were to support the motion rather than oppose it, the conductor would accelerate on its own, generating ever more energy — a perpetual motion machine that contradicts the fundamental laws of physics.
Induction by Motion vs. Induction by Field Change
The animation shows a classic case of induction: a conductor is moved through a static magnetic field. But this is only one of two ways in which induction can occur.
Case 1 — Moving conductor in a static field (this animation): The conductor moves while the magnetic field remains unchanged. The Lorentz force on the electrons in the moving conductor causes the charge separation. This principle is used in generators and dynamos.
Case 2 — Stationary conductor in a changing field: The conductor remains stationary, but the magnetic field around it changes — for example, because a magnet is moved or because an alternating current flows in a neighboring coil. An induced voltage is also produced here. This principle is used in transformers and wireless chargers.
Physically, the law of induction Uind = −ΔΦ/Δt describes both cases equally: what matters is solely that the magnetic flux through the conductor loop changes — whether through movement of the conductor or through a change in the field.
Common Misconceptions
There are several widespread misunderstandings about electromagnetic induction that cause particular confusion when learning:
“Induction generates current.” — Not directly. Induction first produces a voltage (the induced voltage). A current only flows when the conductor is part of a closed circuit. An open conductor moved through a magnetic field shows a measurable voltage between its ends, but no current flows.
“The stronger the magnet, the more voltage.” — This is only true if the conductor is actually being moved. A conductor that rests in even the strongest magnetic field produces no induced voltage. What matters is the change in magnetic flux, not the absolute strength of the field.
“The current always flows in the same direction.” — The direction of the induced current depends on the direction of movement. If the conductor in the animation is moved to the right, the current flows in one direction; if moved to the left, the current direction reverses. This principle is the basis for alternating current generation in generators.
“The Lorentz force drives the conductor.” — The opposite is true. The Lorentz force on the current-carrying conductor acts against the motion (Lenz’s law). It is the reason why work must be done to generate electrical energy.
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Overview and Download
| Title | Electromagnetic Induction 1 |
| Target Audience | Teachers and Lecturers |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version-dependent) |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Freeware |
| Download | Contact |
Contributors
C. Hein, S. Rikowski
Sources
- Authoring tool: Adobe Animate
- 3D engine for 3D model: Papervision3D 2.0
- 3D rotations: Algorithm adopted from Federico Calvo: http://blog.federicocalvo.com/2009/03/papervision-3d-sphere-globla-axis.html
- Curved field lines: Bezier3D class by Aleksandar Mancic
- Authoring tool (control elements included): Adobe Animate
Version History
| Date | Change |
| 2014-06-01 | First version |
| 2024-02-09 | New player application and minor corrections |