Engineering Electromagnetics Fundamentals Flashcards

Stokes' theorem relates a surface integral of the curl of a vector field to:

Answer: A line integral around the bounding contour

Stokes' theorem states ∬(∇×A)·dS = ∮A·dl, converting a surface integral to a closed line integral.

For a uniform plane wave propagating in the +z direction, if E is in the x̂ direction, then H is in the direction:

Answer: +ŷ

For a +z propagating wave, E × H must point in +z, so H = ŷ (since x̂ × ŷ = ẑ).

The inductance per unit length of a two-wire transmission line with wire radius a and separation d (d >> a) is approximately:

Answer: μ ln(d/a) / π

For a two-wire line, L/l = (μ/π) ln(d/a), derived from the magnetic flux linkage per unit length.

In electrostatics, Laplace's equation ∇²V = 0 applies in regions where:

Answer: There is no free charge density

Laplace's equation holds in source-free regions (ρᵥ = 0), while Poisson's equation applies where ρᵥ ≠ 0.

The reflection coefficient Γ at a transmission line load is defined as:

Answer: Γ = (Z_L - Z₀) / (Z_L + Z₀)

The voltage reflection coefficient is Γ = (Z_L − Z₀)/(Z_L + Z₀), determining the reflected wave amplitude.

The normal component of B across a boundary between two magnetic media satisfies:

Answer: B_n1 = B_n2

Since ∇·B = 0, the normal component of B is continuous: B_n1 = B_n2.

The Poynting vector S represents:

Answer: Power flow per unit area (W/m²)

The Poynting vector S = E × H gives the instantaneous power flow per unit area in W/m².