Using Maxwell's equations, derive the expression of the generic wave equation, for a perfect dielectric, and...
Using Maxwell's equations, derive the expression of
the generic wave equation, for a perfect dielectric, and a
conducting media.
Hence derive the expressions for alpha and beta for a perfect
dielectric, and a conducting media.
Homework Answers
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Using Maxwell's equations, derive the expression of
the generic wave equation, for a perfect dielectric, and...
Use Maxwell's Equations to derive a decoupled set of wave equations for electric and magnetic fields...
Use Maxwell's Equations to derive a decoupled set of wave equations for electric and magnetic fields in a linear, homogeneous, isotropic media characterized by (µ, ε, σ) in the absence of sources. Then modify these equations to describe waves propagating in free space. Show all work, please
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that t...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that the electric field E(x, y, z, t) in a conductive material with conductivity σ satisfies the following wave equation a. 72 _ με.at? _ μσαί)F-0 b. Show that the following is a solution E(F, t)-(8 + 9) Eo e-kız cos(at-kez) where Eo is a constant and kR and k, are given by 0.5 w22 c. Obtain the direction of propagation for the wave in part...
Derive the time-independent Schrödinger equation from the classical nondispersive wave equation and a generic standing wave.
Derive the time-independent Schrödinger equation from the classical nondispersive wave equation and a generic standing wave.
9. (a)Using the Maxwell's equations prove that the wave equations for the electric and magnetic fields...
9. (a)Using the Maxwell's equations prove that the wave equations for the electric and magnetic fields are given by 0t2 where l/c-μοεο
Derive the Fresnel equations for reflection and refraction at the boundary of two linear, dielectric media...
Derive the Fresnel equations for reflection and refraction at the boundary of two linear, dielectric media for the case of the monochromatic, plane wave which is linearly polarized in the direction perpendicular to the plane of incidence.
Please Show Work Clearly. 12.3 Time-Harmonic Wave Equation. Using the source-free Maxwell's equations, show that a...
Please Show Work Clearly.
12.3 Time-Harmonic Wave Equation. Using the source-free Maxwell's equations, show that a Helmholtz equation can be obtained in terms of the magnetic vector potential. Use the definition B = V X A and a simple medium (linear, isotropic, homogeneous material). Justify the choice of the divergence of A.
Winter 2005 Q.8 (a) Derive an expression for self inductance per unit length of a parallel...
Winter 2005 Q.8 (a) Derive an expression for self inductance per unit length of a parallel wire of radius a separated by a distance D, where one wire is a return circuit for the current in the other. (b) Using Maxwell's curl equations derive the wave equation in H for a plane wave travelling in the positive x direction in a medium with constants u = Ho E = €, and o = 0. The electric field is in the...
Part # II: (2 Marks) An EM field is said to be nonexistent or not Maxwellian...
Part # II: (2 Marks) An EM field is said to be nonexistent or not Maxwellian if it fails to satisfy Maxwell's equations and the wave equations derived from them. Using the answers in part 1, show that the following magnetic field in a certain dielectric material satisfies all Maxwell's equations (part a) and find the corresponding phase constant B (part b). The magnetic field is given by H(y,t) = 5 cos (2nft + By)a, A/m for which = 480,...
A free electron is described by the wave function: Using the linear momentum operator, derive an expression for the mo...
A free electron is described by the wave function:
Using the linear momentum operator, derive an expression for
the momentum of the electron. Is your answer consistent with de
Broglie's equation?
Write answers clearly on the sheet. Show all working and underline your final answer 1. A free electron is described by the wave function, *(x) = Ae ** Using the linear momentum operator, P = -ih d/dx, derive an expression for the momentum of the electron. Is your answer...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wav...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wavenumber, k, as a function of a, is given by the dispersion relationship ex ωε ωε where σ is the conductivity, μ is the permeability and ε is the permittivity of the conducting medium. (Hint: start with Maxwell's equations, and develop an equation of the form, V" E -k 2 E ). (3 marks) (b) Write down an expression for the physical electrical field...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that the electric field E(x, y, z, t) in a conductive material with conductivity σ satisfies the following wave equation a. 72 _ με.at? _ μσαί)F-0 b. Show that the following is a solution E(F, t)-(8 + 9) Eo e-kız cos(at-kez) where Eo is a constant and kR and k, are given by 0.5 w22 c. Obtain the direction of propagation for the wave in part...
9. (a)Using the Maxwell's equations prove that the wave equations for the electric and magnetic fields are given by 0t2 where l/c-μοεο
Please Show Work Clearly.
12.3 Time-Harmonic Wave Equation. Using the source-free Maxwell's equations, show that a Helmholtz equation can be obtained in terms of the magnetic vector potential. Use the definition B = V X A and a simple medium (linear, isotropic, homogeneous material). Justify the choice of the divergence of A.
Winter 2005 Q.8 (a) Derive an expression for self inductance per unit length of a parallel wire of radius a separated by a distance D, where one wire is a return circuit for the current in the other. (b) Using Maxwell's curl equations derive the wave equation in H for a plane wave travelling in the positive x direction in a medium with constants u = Ho E = €, and o = 0. The electric field is in the...
Part # II: (2 Marks) An EM field is said to be nonexistent or not Maxwellian if it fails to satisfy Maxwell's equations and the wave equations derived from them. Using the answers in part 1, show that the following magnetic field in a certain dielectric material satisfies all Maxwell's equations (part a) and find the corresponding phase constant B (part b). The magnetic field is given by H(y,t) = 5 cos (2nft + By)a, A/m for which = 480,...
A free electron is described by the wave function:
Using the linear momentum operator, derive an expression for
the momentum of the electron. Is your answer consistent with de
Broglie's equation?
Write answers clearly on the sheet. Show all working and underline your final answer 1. A free electron is described by the wave function, *(x) = Ae ** Using the linear momentum operator, P = -ih d/dx, derive an expression for the momentum of the electron. Is your answer...
2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wavenumber, k, as a function of a, is given by the dispersion relationship ex ωε ωε where σ is the conductivity, μ is the permeability and ε is the permittivity of the conducting medium. (Hint: start with Maxwell's equations, and develop an equation of the form, V" E -k 2 E ). (3 marks) (b) Write down an expression for the physical electrical field...
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