Maxwell's Equations (Differential Form)
1. Gauss's Law: \( \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} \)
2. Gauss's Law for Magnetism: \( \nabla \cdot \vec{B} = 0 \)
3. Faraday's Law: \( \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} \)
4. Ampère-Maxwell Law: \( \nabla \times \vec{B} = \mu_0 \left( \vec{J} + \epsilon_0 \frac{\partial \vec{E}}{\partial t} \right) \)
Simulation Formulas (Liénard–Wiechert)
This simulation calculates the E and B fields for a single point charge.
1. Electric Field: \( \vec{E} = \vec{E}_{coulomb} + \vec{E}_{radiation} \)
2. Magnetic Field: \( \vec{B}(\vec{r}, t) = \frac{1}{c} \hat{R}(t_r) \times \vec{E}_{physics}(\vec{r}, t) \). Note \(|\vec{B}| = |\vec{E}| / c\).
Fields use "retarded time" \( t_r = t - r/c \). B-field vectors are scaled visually using the "B-Field Visual Scale" slider. The "Spinning" presets are visual only and do not generate fields in this classical model.