Starting from Maxwell's equations V x V × A = V(V· A) – V²A in a vacuum, use the identity and show that the electric and magnetic fields satisfy both the equation of a wave and obtain the speed of that wave in the MKS system.
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- A traveling electromagnetic wave in a vacuum has an electric field amplitude of 91.5 V/m. Calculate the intensity ? of this wave. Then, determine the amount of energy ? that flows through area of 0.0203 m2 over an interval of 15.7 s, assuming that the area is perpendicular to the direction of wave propagation.A sinusoidal electromagnetic wave propagates in the +x direction through empty space. Its electric field is described by E = (3.56E4 V/m) × sin ((2.06E11 rad/s) t – (687 rad/m) x ) . What is the magnitude of momentum density (momentum per volume) of this electromagnetic wave (in kg/s·m2)?Please help me with the following question and make sure all parts are correct, thanks The electric field of a sinusoidal electromagnetic wave obeys the equation E=−(355V/m)sin[(5.93×1015rad/s)t+(1.99×107rad/m)x]�=−(355V/m)sin[(5.93×1015rad/s)�+(1.99×107rad/m)�]. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Laser light. part a. What is the amplitude of the magnetic field of this wave? Express your answer in teslas. Part b What is the frequency of the wave? Express your answer in hertz. Part c What is the wavelength of the wave? Express your answer in nanometers. Part d What is the period of the wave? Express your answer in seconds. Part e What is the speed of the wave? Express your answer in meters per second.
- Three electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P. E₁ (5.0 x 10-5 V/m) sin[(3.0 x 1014 rad/s)t] -E2= (6.0 x 10-6 V/m) sin((3.0 x 1014 rad/s)t + 45°] E3 = (6.0 x 10-6 V/m) sin[(3.0 x 1014 rad/s)t-45*] E = ( i i ✓) sin[(i x 1014 )t +A certain guided wave travels through air with the following magnetic field H=10+ y cos(157x) sin[(67×10° rad/s)t - Bz] [A/m] (0.3) Find the associated and B. There are a couple ways to solve this problem. Note: this is NOT a plane wave, and be sure to understand why. Nevertheless it IS a valid solution of Maxwell's equations. You will see how guided waves like this come about