The answer is: Using the stress-energy tensor, find an expression of the energy for the electromagnetic...
Using the stress-energy tensor, find the total momentum in absence of current and explain what known physics quantity is.
Question 1: Stress tensor for a parallel plate capacitor Consider an infinite parallel-plate capacitor, with the lower plate (at = = -d/2) carrying the charge density - and the upper plate (at z =d/2) carrying the charge density o. (a) Determine all nine elements of the Maxwell stress tensor (i) for -1 <d/2 and (ii) for : > d/2. (b) Use the stress tensor to find the force per unit area acting on the top plate. (C) Find the electromagnetic...
The electric field of a plane electromagnetic wave in vacuum is Ē = Ēo cos(kz – wt), [1] where Ēo = (3î + 4ỹ) Vm-1 (a) Write down the expression for the magnetic field of this wave. (b) Compute the Maxwell tensor of the wave and provide a physical interpretation of your results. (c) If the frequency of the waves is f = 2.5 x 10Hz what is the energy density in the waves at t= 0 and z= 2.0...
Given that the -field of an electromagnetic wave in vacuum is write an expression for the associated -field. What is the direction of propagation?
Electromagnetic wave has an average energy density of 2.0 J/m3 . A) Find the electric field amplitude. Answer in V/m B) Find the magnetic field amplitude. Answer in mT C) By what factor must the field amplitudes be increased if the average energy density is to be doubled to 4.0 J/m3 ?
4 Stress Tensor 1. Given: T=14 1 01 MPa. 0 0 1 (a) find the stress vector on the plane whose normal is in the direction of +ý (b) Find the normal stress on the same plane. (c) Find the magnitude of the tangential stress on the same plane. (d) Find the three principal directions of stress. Hint: the determinant of a 3 x3 11 a12 13 det a a2 a23a11 (a22033-a3223) a12 a1a33-a31a23)+a13(a2132-a31022) 031 a32 33 Given the following...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
5. Electromagnetic wave in a conductor (10 points) Assume that there is an electromagnetic wave in a conductor with conductivity o, permit € and permeability u. It can be shown that the complex expression for the electrici Ē(2,t) = Ēoe-kzei(kz-wt) g where Eo is independent of x, y, z, t, (10) and --- + [v1 + (9* - )" (11) a) (4 points) Show that the associated magnetic field is: B(3,t) =***Ẽoe-v=ei(k=-ut); (12) b) (6 points) Assume that Eo is...
2. Using Maxwell's stress tensor, calculate the force per unit length of electric attraction between the two parallel wires that each carry a linear charge density separated by a distance 2a. (Hint. Integrate along a plane equidistant between the wires.]
Which of the following are true about the energy of electromagnetic waves in free space? A.Doubling the intensity of an electromagnetic wave doubles the amplitude of the magnetic field. B.The instantaneous energy density of the magnetic field is . C.The average intensity of an electromagnetic wave is . D..The time average of is .