Interactive simulations & visualizations
Visualizing the beauty in physics and mathematics
Project maintained by zhendrikse Hosted on GitHub Pages — Theme by mattgraham
Faraday's law of induction
🎯 Visualization of the relationship between a changing magnetic field and the induced electric field
🧠 Inspired by original version on web page of Rob Salgado
🐍 A VPython demo is available as well, see faradays_law.py
👉 Current through a real wire would have an azimuthal magnetic around the wire
👉 Faraday’s law
🔴 Arrows represent the magnetic field change $\frac{\partial \vec{B}}{\partial t}$
🔵 Arrows represent induced electric field $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$
🟡 Balls visualize the electric charges traveling through the wire.
🟢 Faraday loops represent the orientation of the integration loop used in Faraday’s law.
These green arrows do not necessarily represent the physical electric field direction itself. Instead, they define the positive circulation direction according to the right-hand rule:
Important conceptual points
The simulation distinguishes between:
| Visual Element | Meaning |
|---|---|
| Green loop direction | chosen mathematical orientation |
| Blue electric field | physical induced field |
| Red magnetic arrows | changing magnetic flux source |
This separation is important because Faraday’s law relates:
- the circulation of the electric field around a closed path,
- to the time rate of change of magnetic flux through that path.
Physical Interpretation of the Minus Sign
The minus sign in Faraday’s law means:
Nature resists changes in magnetic flux.
If the magnetic field through the loop increases in one direction, the induced electric field circulates in the direction that would generate an opposing magnetic field. This is the essence of electromagnetic induction and energy conservation.
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