---
tags:
  - science/physics
  - laws
  - electromagnetism
  - maxwell
created: 2026-05-16
breadcrumb: "Physics > Laws of physics > Maxwell's equations"
---

# Maxwell's equations

> **Mechanism:** Foundations of classical electromagnetism

## Items

- **Gauss's law** — ∇·E = ρ/ε₀ — electric charge produces an electric field.
- **Gauss's law for magnetism** — ∇·B = 0 — no magnetic monopoles; magnetic field lines form closed loops.
- **Faraday's law** — ∇×E = −∂B/∂t — a changing magnetic field induces an electric field.
- **Ampère–Maxwell law** — ∇×B = μ₀J + μ₀ε₀ ∂E/∂t — currents and changing E-fields produce magnetic fields.

## Related

- [[famous-physics-equations]]
- [[radio-microwave-thz]]