The magnetic field in a plane monochromatic electromagnetic wave with wavelength
ID: 1998109 • Letter: T
Question
The magnetic field in a plane monochromatic electromagnetic wave with wavelength lambda = 516 nm, propagating in a vacuum in the z-direction is described by B = (B_1 sin(kz - omega t))(i + j) where B_1 = 4.4 times 10^-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. What is k, the wavenumber of this wave? What is z_max, the distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t = 0? What is E_max, the amplitude of the electric field oscillations? What is E_y, the y-component of the electric field at (x = 0, y-0, z = z_max) at t = 0? Which of the following equations describes the spatial and time dependence of the electric field oscillations? E = {E_max/Squareroot 2 sin (kz - wt)} (i + j) E = {E_max/Squareroot 2 sin (kz - wt)} (i - j) E = {E_max/Squareroot 2 sin (kz - wt)} (j + i) E = {E_max/Squareroot 2 cos (kz - wt)} (i + j) E = {E_max/Squareroot 2 cos (kz - wt)} (i - j) E = {E_max/Squareroot 2 cos (kz - wt)} (j + i) v/hat is t_max, the first time after t = 0, when the magnitude of the electric field at the origin (x = y = z = 0) has its maxiumum value? Compare E_x1 and E_x2, the values of the x-component of the electric field at t = 0. E_x1 is evaluated at (x = 0, y = 0, z = z_max), while E_x2 is evaluated at (x = lambda nm, y = lambda nm, z = z_max). E_x1 E_x2Explanation / Answer
1) k =1/wavelength = 1/516e-9
= 1937984 m^-1
2) kz = pi/2
z = pi/2k
= 516e-9*pi/2
= 8.1*10^-7 m
3) Emax = cBmax
= 3e9*4.4e-6*sqrt 2
= 1867 N/C
4) By = [1867/ ( sqrt 2)] sin pi/2 j
= 1320 N/C
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.