Electromagnetism: Waves and Wave Equations
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Questions and Answers

What is the solution to the equation 2E s  E s  0?

  • E s(z) = Eo e^(-z) - Eo' e^(z)
  • E s(z) = Eo e^(-z) + Eo' e^(z) (correct)
  • E s(z) = Eo e^(z) - Eo' e^(-z)
  • E s(z) = Eo e^(z) + Eo' e^(-z)

What is the physical significance of the term  in the expression E xs (z) = Eo e^(-z) e^(-jz)?

  • Wavelength
  • Attenuation constant (correct)
  • Frequency
  • Phase constant

What is the direction of the electric field vector in the electromagnetic wave equation?

  • Propagation axis
  • Vibration axis (correct)
  • Axial direction
  • Radial direction

What is the purpose of inserting the time factor ejωt in the electromagnetic wave equation?

<p>To obtain a complete electromagnetic wave equation (C)</p> Signup and view all the answers

What is the direction of the magnetic field vector in the electromagnetic wave equation?

<p>Perpendicular to the electric field vector (B)</p> Signup and view all the answers

What is the significance of the term Eo' = 0 in the solution E xs (z) = Eo e^(-z) + Eo' e^(z)?

<p>The solution is finite at infinity (C)</p> Signup and view all the answers

What is the condition for the electric wave equation in vacuum and free space?

<p>ρv = 0 and σ = 0 (D)</p> Signup and view all the answers

What is the speed of the electromagnetic wave in vacuum?

<p>u = 1 / √(με) (B)</p> Signup and view all the answers

What is the form of the electric wave equation in one dimension?

<p>∇²E - με (∂²E / ∂t²) = 0 (A)</p> Signup and view all the answers

What is the assumption made about the wave in the electric wave equation?

<p>The wave is in one dimension (A)</p> Signup and view all the answers

What is the form of the magnetic wave equation?

<p>∇²B - με (∂²B / ∂t²) = 0 (A)</p> Signup and view all the answers

What is the phasor form of the electric wave equation?

<p>∂²Ez / ∂z² + jωEz = 0 (B)</p> Signup and view all the answers

What is the expression for u in terms of λ, T, and f?

<p>u = λfT (C)</p> Signup and view all the answers

What is the value of β in terms of ω, λ, and f?

<p>β = ω / (2πλf) (D)</p> Signup and view all the answers

What is the characteristic of a lossy dielectric medium?

<p>It is a partially conducting medium with σ ≠ 0, ε ≠ 0, μ ≠ 0 (D)</p> Signup and view all the answers

What is the curl of curl Es in a linear, isotropic, homogeneous, lossy dielectric medium?

<p>∇ × ∇ × Es = -jωμ(∇ × Hs + Js + jωDs) (C)</p> Signup and view all the answers

What is the resulting equation using the vector identity ∇ × (∇ × A) = ∇(∇ · A) - ∇²A?

<p>∇²Es + jωμ(σ + jωε)Es = 0 (A)</p> Signup and view all the answers

What is the name of the equation ∇²Es - γ²Es = 0?

<p>Helmholtz's equation (D)</p> Signup and view all the answers

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