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 2π n
V = 110cos 120 t +  and n = 01, , …, N − 1
n  N 

While the sum of the voltage of all the lines is zero, the instantaneous power
is not. Find the total power, assuming that the power from each line is pro-
portional to the square of its time-dependent expression. (Hint: Use the dou-
ble angle formula for the cosine function.)

N−1

pt( ) = A cos ω t + 2π n  and P = ∑ p
2
2
n  N  n
n=0
NOTE Another designation in use for a 110-V line is an rms value of 110, and
not the value of the maximum amplitude as used above.

6.7 Interference and Diffraction of Electromagnetic Waves

6.7.1 The Electromagnetic Wave
Electromagnetic waves (em waves) are manifest as radio and TV broadcast
signals, microwave communication signals, light of any color, X-rays, γ-rays,
etc. While these waves have different sources and methods of generation and
require different kinds of detectors, they do share some general characteris-
tics. They differ from each other only in the value of their frequencies. Indeed,
it was one of the greatest intellectual achievements of the 19th century when
Maxwell developed the system of equations, now named in his honor, to
describe these waves’ commonality. The most important of these properties
is that they all travel in a vacuum with, what is called, the speed of light c (c
= 3 × 10 m/s). The detailed study of these waves is the subject of many elec-
8
trophysics subspecialties.
Electromagnetic waves are traveling waves. To understand their mathe-
matical nature, consider a typical expression for the electric field associated
with such waves:

E(z, t) = E cos[kz – ωt] (6.73)
0
Here, E is the amplitude of the wave, z is the spatial coordinate parallel to
0
the direction of propagation of the wave, and k is the wavenumber.

© 2001 by CRC Press LLC