Home exercise 2 2 𝑉𝑉 �� � 1. Suppose 𝑬𝑬(𝑧𝑧, 𝑡𝑡) = 6.0 𝑐𝑐𝑐𝑐𝑐𝑐 �2𝜋𝜋108 𝑡𝑡 − 3 𝜋𝜋𝜋𝜋� 𝒚𝒚 𝑚𝑚 Determine the wave amplitude, frequency, phase constant, wavelength and propagation velocity. Find 𝑯𝑯(𝑧𝑧, 𝑡𝑡). 2. The safety limit for the power density associated with an electromagnetic wave radiated by cellular telephones is recommended at 1 𝑚𝑚𝑚𝑚/𝑐𝑐𝑐𝑐2. If the approximate electric field strength of the cell phone signal is 500 𝑚𝑚𝑚𝑚/𝑚𝑚 and you are using the phone in air, compute the time-average power density and determine whether it satisfies the above safety limit. 3. A 100 𝐻𝐻𝐻𝐻 electromagnetic wave is propagating vertically down into seawater, which is characterized by 𝜇𝜇0 , 𝜖𝜖𝑟𝑟 = 81, 𝜎𝜎 = 4 𝑆𝑆/𝑚𝑚. The electric-fields intensity measured just beneath the surface of the seawater is 1 𝑉𝑉/𝑚𝑚. Find the intensity at a depth of 100 𝑚𝑚. 4. A space boat is to be designed such that the solar radiation power on its sail counters the sun’s gravitational force. Assume that total weight of the boat is 1000 𝑘𝑘𝑘𝑘. Calculate the surface area of the sail. Note: The mean distance between earth and sun is 1.5𝑥𝑥1011 𝑚𝑚, the mass of the sun is 1.99𝑥𝑥1030 𝑘𝑘𝑘𝑘, the gravitational constant is 6.67𝑥𝑥10−11 𝑚𝑚/𝑠𝑠 2 , the total solar radiation power density on earth is 1.4 𝑘𝑘𝑘𝑘/𝑚𝑚2 .
