Electromagnetic Theory
Electromagnetic Theory in GATE PH tests Maxwell's equations, boundary conditions, scalar and vector potentials, gauge choices, Poynting's theorem, plane waves, waveguides, and radiation. Numerical questions often ask for a reflection coefficient, skin depth, cutoff frequency, or energy density.
Core rules and concepts
- Maxwell's equations in vacuum and in matter; in a linear medium D = εE and B = μH. At an interface with no free surface charge, D_n is continuous; with no free surface current, H_t is continuous. E_t and B_n are always continuous.
- The wave equation in a medium has phase velocity v = 1/√(με). For a conductor, the skin depth is δ = √(2/(μσω)).
- Poynting vector S = E × H gives energy flux; the time-averaged magnitude for a plane wave is ½E₀H₀.
- Potentials: B = ∇×A and E = -∇φ - ∂A/∂t. The Lorenz gauge imposes ∇·A + (1/c²)∂φ/∂t = 0 and gives decoupled wave equations.
- In a rectangular waveguide, the cutoff frequency depends on the transverse mode indices and the guide dimensions.
Worked example
A plane wave in vacuum is normally incident on a nonmagnetic dielectric with refractive index n. The electric-field reflection coefficient is r = (1 - n)/(1 + n), and the reflectance is R = r². The transmittance is T = 4n/(1 + n)², so R + T = 1. For n = 1.5, r = -0.5/2.5 = -0.2, R = 0.04, and T = 0.96. The negative sign means a 180° phase reversal on reflection.
Traps that cost marks
- Applying D_n continuity when free surface charge is present.
- Mixing the signs of the reflection coefficient for E and H.
- Forgetting that the skin depth decreases with increasing frequency.
- Using the vacuum wave speed in a medium without dividing by √(ε_rμ_r).