Core Theory II – Electromagnetic Theory
(B.Tech / B.E. – Core Science)
Goal of this chapter
Understand how electric and magnetic fields are generated, how they interact, and how they propagate as waves.
Master Maxwell’s equations, their physical meaning, and basic applications in engineering.
1. Simple Explanation
Electromagnetism is the branch of physics that studies the relationship between electric charges, electric fields, magnetic fields, and how they change in space and time.
- Electric charges create electric fields (E).
- Changing magnetic fields create electric fields (Faraday’s law).
- Changing electric fields create magnetic fields (Maxwell’s addition to Ampère’s law).
- Together, these fields can travel through space as electromagnetic waves (light, radio, X‑ray, etc.).
Maxwell’s equations mathematically express all these facts in four compact vector equations.
2. Key Points
| Topic | What to Remember |
|---|---|
| Maxwell’s Equations | 4 equations: Gauss’s law, Gauss’s law for magnetism, Faraday’s law, Ampère‑Maxwell law. |
| Units | SI – E in V/m, B in T, D in C/m², H in A/m. |
| Vacuum constants | ε₀ = 8.85×10⁻¹² F/m, μ₀ = 4π×10⁻⁷ H/m, c = 1/√(ε₀μ₀) ≈ 3×10⁸ m/s. |
| Wave equation | ∇²E = μ₀ε₀ ∂²E/∂t² (similar for B). |
| Propagation speed | v = 1/√(με) – depends on medium’s permittivity (ε) and permeability (μ). |
| Boundary conditions | Tangential E and H continuous across interface; normal D and B continuous (except surface charges/currents). |
| Poynting vector | S = E × H → energy flux of EM wave. |
| Applications | Transmission lines, antennas, optics, waveguides, magnetic resonance imaging, etc. |
3. Worked Example
Problem:
A plane electromagnetic wave of frequency f = 5 GHz propagates in a non‑conducting medium with relative permittivity εᵣ = 4 and relative permeability μᵣ = 1. The electric field amplitude is E₀ = 10 V/m.
- Find the magnetic field amplitude B₀.
- Determine the wavelength λ in the medium.
- Compute the speed v of the wave.
Step‑by‑Step Solution
1. Speed of the wave
v = 1 / sqrt(μ ε)
Where
- μ = μᵣ μ₀ = 1 × 4π×10⁻⁷ H/m = 4π×10⁻⁷ H/m
- ε = εᵣ ε₀ = 4 × 8.85×10⁻¹² F/m = 3.54×10⁻¹¹ F/m
v = 1 / sqrt( (4π×10⁻⁷) (3.54×10⁻¹¹) )
≈ 1 / sqrt( 4.44×10⁻¹⁷ )
≈ 1 / (6.66×10⁻⁹)
≈ 1.50×10⁸ m/s
So v ≈ 1.5 × 10⁸ m/s.
2. Wavelength
λ = v / f
λ = (1.5×10⁸ m/s) / (5×10⁹ Hz) = 0.03 m