The animation shows how an electric voltage is generated by a rotating magnetic field. In the 3D scene (top left) you can see a cylindrical conductor above a rotating magnet. Inside the conductor, an electric current is induced. This is indicated by blue spheres.
Instructions for Use
Like all animations, the windows can be enlarged or reduced by clicking on them.
You can enlarge and reduce the rectangles in the animation by clicking on them.
After starting the application, you can watch 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.
The Basic Principle – An Intuitive Explanation
A magnet creates a magnetic field with invisible field lines running from the north pole to the south pole. When an electrical conductor is placed in this field and the number of field lines passing through the conductor’s surface area changes, the free-moving electrons in the conductor are set in motion – a current flows.
During rotational motion, this magnetic flux changes continuously: When the magnet is perpendicular to the conductor, the maximum number of field lines pass through the conductor’s surface. When it is parallel, virtually no field lines penetrate the surface. As the rotation continues, the flux changes rhythmically – and this is precisely what generates the alternating voltage that we can observe in the animation.
The induced voltage can be calculated as a function of the angular velocity. The faster the magnetic field rotates, the higher the induced voltage.
\[ U_\text{ind} = \hat{U} \cdot \sin(\omega t) \]
- Û (“U-hat”): the maximum inducible voltage
- sin: the sine function expresses that only the motion occurring perpendicular to the direction of the field lines affects the induced voltage. Motions in the direction of the field lines have no effect.
- ω (omega): the angular velocity
The following applies:
\[ \omega = 2 \pi f \]
- f: the frequency
Note: In the formula above, the expression “ωt” must not be interpreted as a product. It simply represents the angular velocity at time t.
The relationship shown here can also be expressed using the following more fundamental formula (Faraday’s law of induction):
\[ U_\text{ind} = -N \frac{\Delta \Phi}{\Delta t} \]
- N: the number of turns
- ΔΦ / Δt: the change in magnetic flux over time
- − (minus sign): follows from Lenz’s law – the induced voltage always opposes the cause of its creation (conservation of energy)
In technical applications, e.g., in classical generators, conductor windings are used instead of a single conductor, wound multiple times around the magnet.
Why Does the Voltage Follow a Sine Wave?
The sinusoidal voltage results directly from the geometry of rotational motion. Let us consider four key positions of the rotating magnet:
- 0° (starting position): The field lines run parallel to the conductor surface. There is no change in magnetic flux – the induced voltage is zero.
- 90°: The magnet is perpendicular to the conductor. The rate of flux change is at its greatest – the voltage reaches its maximum value Û.
- 180°: Parallel alignment again, the voltage is zero once more.
- 270°: The magnet is perpendicular again, but with reversed polarity – the voltage reaches its minimum −Û.
This pattern – gradual rise, maximum, decline, zero crossing, negative maximum – corresponds exactly to the mathematical sine function.
Note: The animation takes into account the difference between technical and physical current direction. Electrons, indicated by blue spheres, show the physical current direction.
The cross-and-dot symbols refer to the technical current direction.
Rotational Motion vs. Linear Motion
Electromagnetic induction can be produced in two fundamental ways: by linear motion of a conductor through a magnetic field, or by rotational motion.
In linear induction, a straight conductor is moved through a uniform magnetic field. The induced voltage remains constant as long as the speed and field strength do not change. This principle is well suited for understanding the basics of induction (see the animation Conductor in a Magnetic Field).
Rotational motion, as shown in this animation, has a decisive advantage for engineering: it can be maintained continuously. While linear motion eventually reaches its limit and must be reversed, a rotor can spin indefinitely. This is why virtually all generators – from bicycle dynamos to power plant generators – operate on the principle of rotation. The resulting alternating voltage has the characteristic sinusoidal shape.
Where Do We Encounter Electromagnetic Induction?
The principle of induction through rotational motion, as shown in this animation, is one of the most important foundations of modern electrical engineering. Here are some examples:
- Bicycle dynamo: A small magnet rotates past a coil, driven by the motion of the tire, generating the voltage for the bicycle lights.
- Power plant generators: In coal, gas, or nuclear power plants, steam turbines drive large generators that work on exactly the same principle – just on a much larger scale.
- Wind turbines: The wind turns the rotor blades and thus a generator inside the nacelle. Here too, mechanical rotational energy is converted into electrical energy.
- Inductive charging stations: In wireless chargers for smartphones, a coil generates an alternating magnetic field that induces a voltage in a second coil inside the device – without any rotating parts, but based on the same fundamental physical principle.
- Eddy current brakes: In modern trains and roller coasters, induction generates eddy currents in a metal disc that produce a braking effect – entirely without mechanical contact.
Historical Background: Faraday’s Discovery
Electromagnetic induction was discovered in 1831 by the British physicist Michael Faraday. Faraday had no formal mathematical education, but possessed an extraordinary experimental talent and a deep intuitive understanding of physical relationships.
After the Danish physicist Hans Christian Ørsted demonstrated in 1820 that an electric current generates a magnetic field, Faraday asked the reverse question: Can a magnetic field also generate an electric current? After ten years of intensive experimentation, he succeeded in proving that it is not the magnetic field itself, but its change that produces a voltage.
This discovery was revolutionary. It laid the foundation for all electrical power generation as we know it today. Without Faraday’s law of induction, there would be no generators, no transformers, and no electrical grid. The rotational motion of a magnet to generate electricity, as shown in this animation, traces directly back to Faraday’s experiments.
Related Animations
HD Animations
Web Animations
Overview and Download
| Title | Electromagnetic Induction by Rotational Motion |
| 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 the 3D model: Papervision3D 2.0
- Idea and initial concept: Tamara Riehle
- 3D rotations: Algorithm adopted from Federico
Calvo:
http://blog.federicocalvo.com/2009/03/papervision-3d-sphere-globla-axis.html