Question

An Electromagnetic Wave A sinusoidal electromagnetic wave of frequency 43.0 MHz travels in free space in the x-direction as in the figure. At some instant, a plane electromagnetic wave moving in the x direction has a maximum electric field of 725 N/C in the positive y direction. (a) Determine the wavelength and period of the wave. SOLUTION plane. Conceptualize Imagine the wave in the figure moving to the right along the x-axis, with the electric and magnetic fields oscillating in phase. In the figure, the magnetic field is oscillating in the Categorize We use the mathematical representation of the traveling 7 wave model for electromagnetic waves. Analyze Use i = to find the wavelength (in m) of the wave: 1- Cm Find the period T (in s) of the wave as the inverse of the frequency: TE- Cs (b) At some point and at some instant, the electric field has its maximum value of 725 N/C and is directed along the y-axis. Calculate the magnitude and direction of the magnetic field at this position and time. SOLUTION Use "max = c to find the magnitude of the magnetic field (int): Bmax = Emax = 1 Because E and B must be perpendicular to each other and perpendicular to the direction of wave propagation (x in this case), we conclude that B is in the Z-direction . Finalize Notice that the wavelength is several meters. This is relatively long for an electromagnetic wave. As we will see in a subsequent section, this wave belongs to the radio range of frequencies. EXERCISE In SI units, the electric field in an electromagnetic wave is described by the following equation. F = 900 sin(3.80 x 10' x - wt) Hint (a) Find the amplitude (in T) of the corresponding magnetic field oscillations. T (b) Find the wavelength i (in m). in Hz). (c) Find the frequency DHZ

Answer 1

Sel - f - 43.0 MHZ 3.0x108 43.0x106 7 - 0.0698 x 10² 698 6.98 m 43.0x106 0.0233 X 10* = 2.33x10s

6) y-axis Emax - 725 NIC along Bmax Emar 225 24166 X108 Bmax - 62.42x10 s T along 2-axis Exercise Ey - 900 Sin (3.20 x 10?x -wt) Emar - 900 NIC Bomas - [max 900 C 3x100 300 x 10-0 Brun 3.0x10-6 (3) wavelingth is 2 = 20 X-3.00 x 107 2- 25 3.00x10? 2-1.65x10 (0) frequency