Electromagnetism: Waves and Wave Equations

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

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)?

Attenuation constant

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

Vibration axis

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

To obtain a complete electromagnetic wave equation Signup and view all the answers

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

Perpendicular to the electric field vector 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)?

The solution is finite at infinity Signup and view all the answers

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

ρv = 0 and σ = 0 Signup and view all the answers

What is the speed of the electromagnetic wave in vacuum?

u = 1 / √(με) Signup and view all the answers

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

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

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

The wave is in one dimension Signup and view all the answers

What is the form of the magnetic wave equation?

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

What is the phasor form of the electric wave equation?

∂²Ez / ∂z² + jωEz = 0 Signup and view all the answers

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

u = λfT Signup and view all the answers

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

β = ω / (2πλf) Signup and view all the answers

What is the characteristic of a lossy dielectric medium?

It is a partially conducting medium with σ ≠ 0, ε ≠ 0, μ ≠ 0 Signup and view all the answers

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

∇ × ∇ × Es = -jωμ(∇ × Hs + Js + jωDs) Signup and view all the answers

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

∇²Es + jωμ(σ + jωε)Es = 0 Signup and view all the answers

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

Helmholtz's equation Signup and view all the answers