Write down the general mathematical expression for the electric field of a linearly polarised harmonic plane wave propagating in the negative z direction and polarised along the y-axis
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Write down the general mathematical expression for the electric field of a linearly polarised harmonic plane wave propagating in the negative z direction and polarised along the y-axis
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- When a light field is not fully polarized, i.e. its state of polarization possesses some random fluctuations, the Jones vectors are inadequate to describe the polarization properties of the field. One may then use a more general vector known as a Stokes column, written as (E*Ex+EEy) (EEx- EEy) (E* Ey +EEx) -i(EEy – EEx) where the angle brackets ((...)) represent time averaging. The effects of optical devices are described by the use of 4 x 4 matrices known as Mueller matrices. Determine the expressions for the Mueller matrices of: (a) a quarter-wave plate with its fast axis along the x-direction, (b) a linear polarizer aligned at an angle 0 from the x-direction.Consider a coaxial cable of length L with P.E.C. electrodes ending in open circuit. The dielectric in the coaxial cable is od. The radii of the inner and outer conductors are a and b respectively. Assume that the cable is connected to a generator with harmonic voltage with magnitude V. Now analyze the following statements regarding the flux of the Poynting vector p. a- bp is constant along the wire b- If the radii of both conductors is scaled by a factor X, the power flux in the wire scales with the same factor c- The power flux in the middle of the wire (at L/2) is one half of the power flux in the generator d- The power flux in the middle of the wire (at L/2) is one half of the power flux at the end of the cable. (L) Only statement (a) is correct O Only statement (b) is correct O Only statement (c) is correct Only statement (d) is correct Statements (a) and (b) are correct Statements (a) and (c) are correct Are all correct Are all wrong O Other combination not listed in the options…We have a plane wave in vacuum with direction of propagation along the wave vector K and angular frequency w. Eo is a complex but constant vector. Then, the electric field vector is E(r,t)=Re{E0 exp i (k.r-wt)} Deduce the following properties of a plane wave using Maxwell's equations and the material equations a) which condition has to be valid for the vectors k and E relatively to each other? b) calculate the magnetic field induction B in independence on the electric field vector C) calculate the Poynting vector in independence on the electric field vector
- Consider a plane, monochromatic, electromagnetic wave traveling in a homogeneous medium.Its electric field vector E in units of (V/m) is given in the image below where t(sec), and x(m). a) Derive an expression for the magnetic field B->b) Find the direction of the the magnetic field B-> from part a.Problem 1. In class we will consider the sum of the electric field of two plane waves, u:(z.t) and uz(z.t), both traveling in the positive z direction with slightly different frequencies and propagation constants and with equal amplitudes. The electric fields of both plane waves are oriented in the y direction, which means that they have the same "polarization". The time and space variation of the two electric fields are given by: u: (2.1) = cos(@t - kz) uz(2.1) = cos ([o + Ao]t - [k + Ak]2) We will show that the sum of these two waves produce an intensity envelope in time and space that modulates the carrier frequency of m + Ao/2. The velocity of the envelope is called the group velocity. Assume Ao is << than o. For this problem, consider the sum of two slightly different waves with similar electric fields: v.(z) = sin(ot - kz) vz(z1) = sin([o + Ao]t - [k + Ak]z) Derive analytically an expression for a) the group and b) the phase velocity for the sum of the two fields. HINT: sinfa) +…RF Electromagnetics: . If an x-component of the E-field varies as a sine function, and y-field component varies as a cosine function; assuming that the Ex=0.7Ey, what is the polarization of the resultant wave whichpropagates in the positive z-direction. For frequency f, write the full expression for the electricfield of a plane wave propagating in vacuum.
- The amplitude of the electric field of a uniform plane wave propagating in the + z direction is 250V / m. If E-> = Ex x^ (On the image) and w=1.0 Mrad/s find: They ask me for the frequency f of the wave, The wavelength the period and the amplitude of H Please don't skip any steps Please be sure that the answer is fine, no matter how long it takesA uniform plane wave with a frequency of 9375MHz propagates in polystyrene. If the electric field intensity has a maximum amplitude of 20V / m, although it is not a lossless medium, attenuation is neglected for the moment. Therefore your ur = 1 Er = 2.56; find: Phase constant, propagation speed, wavelength and intrinsic impedance. The equations for electric field intensity and magnetic field intensity The Poyting vector equationPlease solve ASAP Problem 1: The electric field in a radio (electromagnetic) plane wave is given by the equation(picture attached) E(x, t) = j0.09 sin(2.1r – 27 × 10^6 t) V/m with a in meters and t in seconds. All parts of this problem refer to this expression. a) What is the direction of propagation of this wave? Choose one: +x -x -y +y +z -z b) What is the polarization? Choose one: X y or z c) What is the wavelength? (Give a number, in meters) d) What is the frequency? (Give a number, in Hz) a) What is the direction of propagation of this wave? Choose one: +x -x -y +y +z -z b) What is the polarization? Choose one: X y or z c) What is the wavelength? (Give a number, in meters) d) What is the frequency? (Give a number, in Hz)
- A parallel plate capacitor with circular plates of radius R=18 cm and plate separation d=7 mm is being charged at the rate of 4.5 C/s. a) What is the displacement current through a circular loop of radius r=5.5 cm centered on the axis of the capacitor? b) What is the displacement current through a circular loop of radius r=23 cm centered on the axis of the capacitor (note that this radius is bigger than the radius of the capacitor)? c) What is the magnitude of the magnetic field between the capacitor plates at a radius r=5.5 cm from the axis of the capacitor?A uniform plane wave, with electric field magnitude of 3 (mV/m), is propagating in a medium with µ, = 4. We know that this plane wave travels at a speed of co/8 where co is the speed of light in vacuum. The frequency of this wave is 1 GHz. The propagation direction is y direction. We also know that this plane wave is an LHCP wave. Find: a) The wavelength of the plane wave in this medium. b) The phasor form of the E field which exhibits all the characteristics given in the problem. c) The magnetic field H in the time domain.A plane wave is propagating in vacuum, and its electric field can be expressed as the following: Ē = (Eoē, + Egē,) sin (wt – kz) where Eo is a real number. (a) What is the propagation direction? (b) Find the complex amplitude of the electric field. (b) Find the complex amplitude of the magnetic field.