1. A time-dependent electromagnetic field is given by, Ē(r,t = 0) = ĉEoe-(z/a)?, H (r,t=0) =...
2. Phasors At a given position x-0 two time-dependent electric fields E,t) and E,(t) interfere: E,(t)-2"cos(ot) and E2(1) = 3~cos(ot-π) Using the method of phasors, a) Evaluate the resultant field EE()+E(t) at that position. b) Using the complex plane, draw the three phasors at two arbitrarily different times. 4 2. Phasors At a given position x-0 two time-dependent electric fields E,t) and E,(t) interfere: E,(t)-2"cos(ot) and E2(1) = 3~cos(ot-π) Using the method of phasors, a) Evaluate the resultant field EE()+E(t)...
Problem 6. Electromagnetic plane waves in a lossy medium The electric field of an electromagnetic plane wave traveling in a lossy medium can be written as where z is the distance, t is time, and fthe frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (i.e., to 1/3 of the amplitude at z-0 when it arrives at z- 100...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m)....
An electromagnetic wave is propagating in the +z direction. The magnetic-field-versus-time graph is shown for the location z = 0. (Please notice the use of 10^-11 s as the unit for time.) What is the frequency of this wave? Explain how you determined your answer. What is the wavelength? Explain how you determined your answer. On the axes provided, sketch the magnetic-field-versus-position graph for this EM wave at the time t = 2 times 10^-11 s. For full points, your...
1. At t t 0, inertial systems S and S' are coincident in a region of electromagnetic field. Afterward, the origin of system S' heads off in the 4th quadrant of the zy plane, moving away from the origin of system S at a speed of c along a line that rnakes an angle of 30° with the +z axis. Suppose that system S measures the field to be purely magnetic, where B-B,Cx (a) Let n be the heading of...
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(t) = (-2 cost, 2 sin t, 2t) 0 < t < 2π (3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83,...
1. A particle, initially (t -> 0) in the ground state of an infinite, 1D potential box with walls at r 0 and = a, is subjected at time t = 0 to a time-dependent perturbation V (r, t) et/7, with eo a small real number a) Calculate to first order the probability of finding the particle in an excited state for t 0. Consider all final states. Are all possible transitions allowed? b) Examine the time dependence of the...
2. A long solenoid carrying a time-dependent current I(t) is wound on a hollow cylinder whose axis of symmetry is the z-axis. The solenoid's radius is a, and it has n turns per metre. (a) * Write down the magnetic intensity H(ที่ t) and magnetic field B(r,t) everywhere. What is the energy density in the magnetic field inside the solenoid? (b Find the electric field E(F,t) everywhere using Faraday's law in integral form. (c) * Find the magnetic vector potential...
8a: a light wave of amplitude E sub 0 = 1 traveling in the +z direction is incident on a slab of glass, refractive index n=1.5, at perpendicular incidence. It has wavelength λ = 2π/k in vacuum. Determine the reflection coefficient, R, and transmission coefficient, T for the wave. b. Now assume that the slab has thickness a, meaning its boundaries are located at z = 0 and z = a. Assume it is infinite in all other directions. In...