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Tarea 1 Electrodinámica Clásica II Instituto de Física y Matemáticas, UMSNH Prof. Juan Carlos Arteaga Velázquez 1. The instantaneous expression for the electric field component of an AM broadcast signal propagating in air is given by Re[E(x, t)] = z 10 cos(1.5π 106 t + bx) V/m, Where z is the unitary vector in direction of z. a) Determine the direction of propagation and frequency ν. b) Write the instantaneous expression for the corresponding magnetic field Re[H(x, t)]. 2. An FM radio broadcast signal traveling in the y direction in air has a magnetic field given by H(y) = (-x + i z) 2.92e-3 exp(-i 0.68π y) A/m, a)Determine the frequency (in MHz) and wavelength (in m). b) Find the corresponding E(y). c) Find the real parts of the electromagnetic fields. 3. The magnetic field component of a UHF electromagnetic signal transmitted by a cellular phone base station is given by H(y) = x 50 exp[-i( 17.3y - π/3)] μA/m, Where the coordinate system is defined such that the z axis is in the vertical direction above a horizontal ground (xy plane or the z = 0 plane). a) Determine the frequency ν and wavelength λ. b) Write the corresponding expression for the electric field, E(y). c) An observer located at y = 0 is using a vertical electric dipole antenna to measure the electric field as a function of time. Assuming that the observer can measure the vertical component of the electric field without any loss, what is the electric field at the time instants corresponding to ωt = 0, π/2, π, 3π/2, 2π. 4. A spaceship in lunar orbit (The Earth-Moon distance is 380e6 m) transmits plane waves with an antenna operating at 1 GHz and radiating a total power of 1 MW isotropically. Find a) the time-average power density and b) the peak electric field value on Earth’s surface, and c) the time it takes for these waves to travel from the spaceship to Earth. 5. Jackson, 3rd edition, Chapter 7, page 340, problems 7.2, 7.3, 7.4, 7.5, 7.7, 7.8.