Download Tarea 1 Electrodinámica Clásica II Instituto de Física y - ifm

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.