Show that the electric field: E(x,t)-E cos(kr-at)+E, cos(kx-of) satisfies Maxwell's equation: Here, ø, and oj are...
10. Show that the electric field:E(x)=Ecos(KX-ar)-E, cos(KX-OM) satisfies Maxwell's equation x, t Here, o and o are two arbitrary frequencies, and remember: o-ck and o-ck2
10. Show that the electric field:E(x)=Ecos(KX-ar)-E, cos(KX-OM) satisfies Maxwell's equation x, t Here, o and o are two arbitrary frequencies, and remember: o-ck and o-ck2
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...
1. Assume that the light of electric field B(x,t) Eo sin(kx - at) coming from the single slit can be divided into N identical waves with electric fields of the form E (x,t) E sin(kx - wt), E2(x, t) B sin (kx- c 2) E(x,t) = wt + - and the phase difference between the first and the Nth E sin kx- wt + waves is . The amplitudes of the electric fields have a relation Eo NE Assume that...
check whether the function E(x,t)= Asin(kx^2-wt^2) satisfies the wave equation. if so, find the wave speed. if not explain
(a) Show that this field can satisfy Maxwell's equations if w
and k are related in a certain way.
(b) Suppose w=1010s-1 and
E0=1kV/m. What is the wavelength? What is the energy
density in joules per cubic meter, averaged over a large region?
From this calculate the power density, the energy flow in joules
per square meter per second.
(c) Show also that the electric field of associated with a
spherically symmetric wave may have the dependence Ei =
{Acos[k(r...
(a) Show that this field can satisfy Maxwell's equations if w
and k are related in a certain way.
(b) Suppose w=1010s-1 and
E0=1kV/m. What is the wavelength? What is the energy
density in joules per cubic meter, averaged over a large region?
From this calculate the power density, the energy flow in joules
per square meter per second.
(c) Show also that the electric field of associated with a
spherically symmetric wave may have the dependence Ei =
{Acos[k(r...
B(, t) = Bmar sin(kx - wt). (e) Using Faraday's law, find the electric field induced by the magnetic wave. (f) In part (e), what is the amplitude of the electric wave? Is there any phase difference between the electric wave and the magnetic wave? (g) The electric field you found in part (e) should also satisfy Ampére-Maxwell equation. Find the speed of the EM wave in terms of the constants en and yo using this requirement.
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
Given the electric field phasor E-E) ρ-le-jkza, in cylindrical coordinates, where 1.4 , show that it represents an electromagnetic wave propagating in free space by using (a) Maxwell's equations, and (b) Helmholtz equation. (c) Find the magnetic field phasor H. 88 8-9 Given the electric field phasor E -(E.a, +jE a)e n free space, determine (a) propagation direction, (b) H, (c) & and (d) polarization state. 1th yeaeo circularly polarized waves.
Given the electric field phasor E-E) ρ-le-jkza, in cylindrical...