An overview of electromagnetic fields, including the fundamental concepts, definitions, and the importance of studying electromagnetic fields in various fields of science and technology.
Introduction to Electromagnetic Fields
Graduate‑level overview – concise, organized, and ready for quick reference.
| Concept | Definition | Symbol | Units |
|---|---|---|---|
| Electric Field | Region of space where a charge experiences a force | E | V · m⁻¹ (N · C⁻¹) |
| Magnetic Field | Region where a moving charge (or current) experiences a force | B | tesla (T) = N·A⁻¹·m⁻¹ |
| Electromagnetic Field | Unified description of E and B that obey Maxwell’s equations | – | – |
| Field Line | Imaginary line tangent to the field vector at every point; density ∝ magnitude | – | – |
| Equation | Physical Meaning | Mathematical Form |
|---|---|---|
| Gauss’s Law (Electric) | Electric flux through a closed surface equals enclosed charge | ∇·E = ρ/ε₀ |
| Gauss’s Law (Magnetic) | No magnetic monopoles; net magnetic flux = 0 | ∇·B = 0 |
| Faraday’s Law | Time‑varying magnetic field induces an electric field | ∇×E = –∂B/∂t |
| Ampère‑Maxwell Law | Currents and changing electric fields produce magnetic fields | ∇×B = μ₀J + μ₀ε₀∂E/∂t |
ε₀ – vacuum permittivity (≈ 8.854 × 10⁻¹² F m⁻¹)
μ₀ – vacuum permeability (4π × 10⁻⁷ H m⁻¹)
ρ – charge density, J – current density.
Starting from curl equations with ρ = 0, J = 0:
Result: E satisfies the wave equation
[ \boxed{\nabla^{2}\mathbf{E} - \mu_{0}\varepsilon_{0}\frac{\partial^{2}\mathbf{E}}{\partial t^{2}} = 0} ]
A similar equation holds for B.
[ c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}} \approx 2.998 \times 10^{8}\ \text{m·s}^{-1} ]
| Quantity | Expression | Interpretation |
|---|---|---|
| Energy density | (u = \frac{1}{2}\varepsilon_{0}E^{2} + \frac |