Consider a plane, monochromatic, electromagnetic wave traveling in a homogeneous medium, with index of refraction n = 1. Its magnetic field vector B in units of T is given by B₁ = 0 B₂ = 0 where t is seconds, and is in meters. a) Derive an expression for the electric field E associated with the magnetic field B₁. B₁ = = -9 × 10-8 sin(0.78x + 3.14 × 10°t)ŷ b) Find the direction of the the electric field E from part a. c) Find the direction of the Poynting vector 5. [1 marks]

The following considers electromagnetic wave propagating in free-space (without charges or currents). (a) State the Maxwell's equations in terms of E and H for the free-space. (b) Should that the four equations are satisfied by: E = Eo cos (w²-t)) x Eo H = COS CHO for some constants Eo and co, where c is the speed of light in free-space. s(w (²-t))ỹ

Consider a plane electromagnetic wave travelling in free space. The magnetic field is given by B = B₁ (x − 2) and electric field is given by E = E₁ (− x + 2 y − 2) . Then the direction of the propaga- tion of the wave is (a) -x-y-2 (b) x + 2y - 22 (c) 2x + y + 22 (d) None of these

The electric field of an electromagnetic plane wave traveling in a vaccum is described by  E(x,y,z,t) = 200 (V/m)ex*ei(ky-ωt) with k = 1.0 * 107/m and ω = 3 * 1015 rad/s Find the vector expression that describes the corresponding magnetic field of this wave.

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 linearly polarized sinusoidal electromagnetic wave moving in the positive x direction has a wavelength of 7.60 mm. The magnetic field of the wave oscillates in the xz plane and has an amplitude of 6.90 µT. The magnitude of the electric field vector for this wave can be written as E = Emax sin(kx – øt). What are the following? (a) the value of Emax 2070 V/m (b) the wave number k 826.73 m-1 (c) the angular frequency w 2.48e11 rad/s (d) the plane in which the electric field oscillates the xz plane the yz plane the xy plane (e) the average Poynting vector (Express your answer in vector form.) Sav 11.37 · 10°i X W/m² (f) the radiation pressure exerted by this wave on a perfectly reflecting lightweight solar sail 3.79e-5 Pa (g) the acceleration of the solar sail if its dimensions are 5.00 m x 8.00 m and its mass is 40.0 g 0.038 m/s²

The electric field of a harmonic plane electromagnetic wave propagating in vacuum is given by (0 , 0 , 4)cos(3x-ωt) V/m; hence the corresponding magnetic field is:

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

A uniform transverse electromagnetic wave is propagating in the z-direction, and its magnetic field component is in the y- direction and given as By = Ho (x²+y+z2) cos(wt). The conduction current density is zero in the medium. What is the magnitude of the displacement current density in Amperes/m² at the point (x,y,z) = (1, 1, 1)? 0.17 O 0.39 0.24 O 0.31 O 0.42

A plane electromagnetic wave is traveling in a vacuum. The magnetic field is directed along the z-axis and given by: B, = 3.0µT sin ((1.0 × 107 )x - (3.0 × 1015 )t ) a) Determine the wavelength , of the wave. b) What is the frequency, f, of the wave in Hertz? c) Determine the maximum strength of the B-field. d) Determine the maximum strength of the E-field and it direction. e) Can you find a time and place when the B-field is zero? f) What is the strength of the E-field when the B-filed is zero?