About Maxwell's Equations

Maxwell's equations are the fundamental laws governing electromagnetism. They describe how electric and magnetic fields are generated and interact. The key equations are:

$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} $$
(Gauss's Law for Electricity)

$$ \nabla \cdot \mathbf{B} = 0 $$
(Gauss's Law for Magnetism)

$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} $$
(Faraday's Law)

$$ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} $$
(Ampère-Maxwell Law)

How the Simulator Works

1. Adjust the Electric Field Strength (V/m) using the slider.
2. Click "Start Simulation" to animate electric field vectors on the canvas.
3. The animation simulates oscillating electric fields, illustrating their spatial and temporal variation.
4. The formulas above are rendered using MathJax to ensure proper display of all special symbols.