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ELECTROMAGNETIC ENGINEERING II

SUMMER 1997

PREVIOUS HOMEWORK ASSIGNMENTS

Assignment 1 (due June 4, 1997):
  1. [10] Ramo, Whinnery & Van Duzer, Problem 1.2d
  2. [20] Ramo, Whinnery & Van Duzer, Problem 1.2e
  3. [10] Ramo, Whinnery & Van Duzer, Problem 1.4a
  4. [10] Ramo, Whinnery & Van Duzer, Problem 1.5a
  5. [10] Ramo, Whinnery & Van Duzer, Problem 1.6a
  6. [10] Ramo, Whinnery & Van Duzer, Problem 1.8e
Assignment 2 (due June 11, 1997):
  1. [10] Ramo, Whinnery & Van Duzer, Problem 1.11a
  2. [10] Ramo, Whinnery & Van Duzer, Problem 1.12b
  3. [10] Ramo, Whinnery & Van Duzer, Problem 1.16a
  4. [10] Find D, E and P for a parallel-plate capacitor with area A and separation d, filled with a dielectric with relative permittivity "epsilon sub r" (HTML doesn't do Greek letters easily yet). Also find the surface charge density on the parallel plates.
  5. [10] Ramo, Whinnery & Van Duzer, Problem 2.2b
  6. [10] Ramo, Whinnery & Van Duzer, Problem 2.2c
  7. [10] Ramo, Whinnery & Van Duzer, Problem 2.4g
  8. [10] Ramo, Whinnery & Van Duzer, Problem 2.5
Assignment 3 (due June 18, 1997):
  1. [10] Ramo, Whinnery & Van Duzer, Problem 2.6a
  2. [10] Ramo, Whinnery & Van Duzer, Problem 2.6b
  3. [10] Ramo, Whinnery & Van Duzer, Problem 2.12a
  4. [10] Ramo, Whinnery & Van Duzer, Problem 2.12b
  5. [10] Ramo, Whinnery & Van Duzer, Problem 3.2b
  6. [20] Ramo, Whinnery & Van Duzer, Problem 3.3a
Assignment 4 (due June 25, 1997):
  1. [10] Ramo, Whinnery & Van Duzer, Problem 3.6c
  2. [10] Ramo, Whinnery & Van Duzer, Problem 3.8c
  3. [10] Ramo, Whinnery & Van Duzer, Problem 3.12e
  4. [10] Ramo, Whinnery & Van Duzer, Problem 3.14
  5. Consider an electric field with the following space and time dependence: 
         Ex = E0 cos (omega t - kz)
     Ey = E0 sin (omega t - kz)
     Ez = 0
     
     Note that omega is a Greek letter, and is not displayable by
     most browsers at this time.
     
     (Browser test: If your browser displays Ex
     as Ex, then it can't display subscripts.  Please interpret
     Ex as E sub x.)
    1. [10] If the phase velocity of the wave is v, find the relation between k and omega.
    2. [10] Find the components of H as functions of z and t.
    3. [10] Draw the E vector in the XY plane at the times t = pi / (2 omega), t = pi / omega, t = 3pi / (2 omega), and t = 2 pi / omega.
    4. [10] Find the components of the Poynting vector as functions of z and t.
Assignment 5 (due July 2, 1997): 
  1. {[20]} Obtain the exponential Fourier series 
of the function $f$ such that
for $x$ in the interval $[-\pi,\,\pi]$,

\begin{equation}
f(x) = e^{-\alpha |x|},
\end{equation}

where $\alpha$ is a positive real constant.


  2. 
{[20]} Sketch (or, if you can, graph on a computer)
the periodic extension of the function defined in Problem 1.

  3. 
{[20]} 
Obtain the exponential Fourier series 
of the function $f$ such that
for $x$ in the interval $[-\pi,\,\pi]$,

\begin{equation}
f(x) = |x|.
\end{equation}


  4. 
{[20]} 
Obtain the exponential Fourier series 
of the function $f$ such that
for $x$ in the interval $[-\pi,\,\pi]$,

\begin{equation}
f(x) = |\sin x|.
\end{equation}
Assignment 6 (due July 9, 1997):
  1. [50] An electromagetic field propagating in a waveguide formed by two parallel, perfectly conducting planes at x = - d/2 and x = d/2 has the following components:
    1. In the dielectric: 
      Ex = - (beta E0d/pi) sin (pi x/d) sin (omega t - beta z)
Ez = E0 cos (pi x/d) cos (omega t - beta z)
Hy = - (epsilon omega E0d/pi) sin (pi x/d) sin (omega t - beta z)
    2. In the conductors: All fields are zero

    The exercise: Find the direction and magnitude of the surface current density (amperes per meter) on the wall at x = d/2, in terms of z and t.

  2. [20] Ramo, Whinnery and VanDuzer, Exercise 3.11c (use the formula for the Laplacian in cylindrical coordinates inside the cover)
  3. [30] Ramo, Whinnery and VanDuzer, Exercise 3.19b
Assignment 7 (due July 16, 1997):
  1. [60] Ramo, Whinnery and VanDuzer, Exercise 8.3b
  2. [30] Ramo, Whinnery and VanDuzer, Exercise 8.3c
Assignment 8 (due July 25, 1997):
  1. [30] Ramo, Whinnery and VanDuzer, Exercise 8.8a
  2. [30] Ramo, Whinnery and VanDuzer, Exercise 8.8c
  3. Obtain and read the file disperse.pdf.
    1. [20] Find the numerical value of beta2 when the value of the chromatic dispersion D is equal to 10 picoseconds per nanometer, per kilometer and the wavelength is 1550 nm. What are the units of beta2?
    2. [20] Find the difference in arrival times of two pulses centered at the wavelengths 1550 nm and 1549 nm after propagation through a distance of 100 km, using the value of D given in part (a).
Assignment 9 (due August 1, 1997):
  1. [30] Ramo, Whinnery and VanDuzer, Exercise 8.7b
  2. [30] Ramo, Whinnery and VanDuzer, Exercise 8.8d