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.
Usage Note
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Explanations
The animation provides an introduction to the operating principle of electrical generators.
The induced voltage can be calculated as a function of the angular velocity. The faster the magnetic field rotates, the higher the induced voltage.
\[ U_\text{ind} = \hat{U} \cdot \sin(\omega t) \]
The symbol Û (“U-hat”) stands for the maximum inducible voltage. The sine function expresses that only the motion occurring perpendicular to the direction of the field lines affects the induced voltage. Motions occurring in the direction of the field lines have no effect. The letter ω (omega) stands for the angular velocity. The following applies:
\[ \omega = 2 \pi f \]
The letter f stands for 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):
\[ U_\text{ind} = -N \frac{\Delta \Phi}{\Delta t} \]
In this formula, the magnitude of the induced voltage is considered as a function of the change in magnetic flux (Delta Phi divided by Delta t) and the number of turns (N). The minus sign originates from the historically incorrect assumption about the direction of electric currents.
In technical applications, e.g., in classical generators, conductor windings are used instead of a single conductor material, looping several times around the magnet.
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.
Overview and Download
| Title | Electromagnetic Induction by Rotational Motion |
| Target Group | Teachers and Presenters |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version dependent) |
| Features | Full-screen mode lossless zoom supports large screens and projectors |
| 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