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\centerline{\bf Electrodynamics A (PHY 5346) Fall 2016 
Classwork and Homework} \bigskip

Every exercise counts 10 points unless stated differently.
\bigskip

{\bf Set 1:}

\begin{enumerate}

\item Exercise E.62: Solenoid. Homework, due 1/17/2017 before class.

\end{enumerate}
\bigskip

{\bf Set 2:}

\begin{enumerate}
\setcounter{enumi}{1}

\item Exercise E.63: Magnetic dipoles. Homework, due 1/19/2017 before class.

\item Exercise E.65: Magnetic moment of a disk. Homework, due 1/19/2017 before class.

\end{enumerate}
\bigskip % \eject

{\bf Set 3:}

\begin{enumerate}
\setcounter{enumi}{3}

\item Exercise E.66: Magnetism in matter. Homework, due 1/26/2017 before class.

\item Exercise E.67: Faraday's law. Homework, due 1/26/2017 before class.

\item Exercise E.68: LCR circuit. Homework, due 1/26/2017 before class.

\item Exercise E.69: Complex numbers and integration. Classwork, 
      due 1/26/2017 in class.

\end{enumerate}
\bigskip % \eject

{\bf Set 4:}

\begin{enumerate}
\setcounter{enumi}{7}

\item Exercise E.70: Generalized Residue Theorem. Homework, 
      due 2/2/2017 before class.

\item Exercise E.71: Green function by Fourier transformation.
      Homework due 2/2/2017 before class.

\item Exercise E.24: Current density of a point charge.
      Homework due 2/2/2017 before class.

\end{enumerate}
\bigskip % \eject

{\bf Set 5:}

\begin{enumerate}
\setcounter{enumi}{10}

\item Exercise E.72: Wave equation with point source.
      Homework, due 2/9/2017 before class.

\item Exercise E.73: Covariant retarded Green function.
      Homework, due 2/9/2017 before class.

\item Four-potential of a moving point particle. 
      Homework, due 2/9/2017 before class.
\smallskip

For simplicity use in this problem $c=1$ for the speed of light
and arbitrary, dimensionless time and distance units.

Let $t$ be the time in an inertial frame $K$. For $t\ge 0$ the speed of 
a point particle in $K$ is given by $\vec{\beta}=\beta\hat{x}^1$ with 
$\beta=\beta(t)=\tanh(t)$ and its initial position at time $t=0$ is at 
the origin $\vec{r}_0=\vec{0}$. All questions are with respect to the
$K$ frame.

\begin{enumerate} 
\item Find the distance of the particle from the origin, $r(t)=r^1(t)$,
      as function of the time.
\item Evaluate $\beta(t_1)$ and $r(t_1)$ numerically for $t_1=0.6931472$.
\item At which time $x^0$ does an observer at the origin $\vec{x}=0$ 
      observe the electromagnetic potentials which correspond to the 
      position $r(t_1)$ of the point particle?
\item Take $q_e$ for the charge of the point particle and find the
      electromagnetic potentials, which are observed at the space-time
      point defined by $x^0$ from (c) and $\vec{x}=0$.
You may use
\begin{eqnarray} \nonumber
  \Phi\left(x^0,\vec{x}\right) = \left[\frac{q}{\left(1-
  \vec{\beta}\cdot\hat{n}\right)\,R}\right]_{\rm ret}\!\!,~~~
  \vec{A}\left(x^0,\vec{x}\right) = \left[\frac{q\,\vec\beta}{\left(
  1-\vec{\beta}\cdot\hat{n}\right)\,R}\right]_{\rm ret}\!\! ,
\end{eqnarray}
or, equivalently,
\begin{eqnarray} \nonumber
  A^{\alpha} (x)\ =\ \frac{q\,U^{\alpha}(\tau^0)}{
  \left[x-r(\tau^0)\right]^{\beta}\,U_{\beta}(\tau^0)}\,.
\end{eqnarray}
\end{enumerate}
\end{enumerate}

{\bf Set 6:}

\begin{enumerate}
\setcounter{enumi}{13}

\item Exercise E.74: Charge conjugation, parity and time reveersal
      in electrodynamics.  Homework, due 2/16/2017 before class.

\item Exercise E.76: Proca Lagrangian. Homework, due 2/16/2017 
      before class.

\item Exercise E.75: Electromagnetic energy-momentum tensor. 
      Homework, due 2/16/2017 before class.

\end{enumerate}

{\bf Set 7:}

\begin{enumerate}
\setcounter{enumi}{16}

\item Exercise E.77: Lorentz force and energy-momentum tensor.
      Homework, due 3/2/2017 before class.

\item Exercise E.78: Field energy of a sphere.
      Homework, due 3/2/2017 before class.

\item Exercise E.82: Covariant derivation of the wave equation
      for fields. Homework, due 3/2/2017 before class.

\end{enumerate}

{\bf Set 8:}

\begin{enumerate}
\setcounter{enumi}{19}

\item Exercise E.80: 1D wave equation for a dispersive medium.
      Homework, due 3/9/2017 before class. 

\item Exercise E.83: Energy density and Poynting vector for 
      plane waves.  Homework, due 3/9/2017 before class. 

\item Exercise E.89: Reflection and transmission of a circularly
      polarized wave. Homework, due 3/9/2017 before class. 

\end{enumerate}


{\bf Set 9:}

\begin{enumerate}
\setcounter{enumi}{22}

\item Exercise E.84: Wave with a finite transverse extension.
      Homework, due 3/23/2017 before class. 

\item Exercise E.90: A model for dispersion.
      Homework, due 3/23/2017 before class. 

\item Exercise E.91: Faraday Effect.
      Homework, due 3/23/2017 before class. 

\item Exercise E.93: Principal value integral (1) and (2).
      Classwork, due 3/21/2017 in class, 5~points. 

      Exercise E.93: Principal value integral (3).
      Homework, due 3/23/2017 in class, 5~points. 

\end{enumerate}


{\bf Set 10:}

\begin{enumerate}
\setcounter{enumi}{26}

\item A. Exercise E.93: Principal value integral (4) and (5).
      Look up the Typos Corrections as posted on the Web!

      B. Show the fall-off behavior $|\epsilon_0(\omega_R)-1| 
      \sim 1/|w_R|^2$ for $\omega_R\to\infty$.

      Homework, due 3/30/2017 in class.

\item Exercise E.92: A relation for the group velocity.
      Homework, due 3/30/2017 before class. 

\item Exercise E.94: Kramers-Kronig relation for a model.
      Homework, due 3/30/2017 before class. 

\end{enumerate}


{\bf Set 11:}

\begin{enumerate}
\setcounter{enumi}{29}

\item Exercise E.95: Skin depth.
      Homework, due 4/6/2017 before class. 

\item Exercise E.96: TM waves in a rectangular wave guide.
      Homework, due 4/6/2017 before class. 

\item Exercise E.99: Cubic cavity oscillator.
      Homework, due 4/6/2017 before class. 

\end{enumerate}

{\bf Set 12:}

\begin{enumerate}
\setcounter{enumi}{32}

\item Exercise E.97: Cylindrical wave guide: $\rm T_{11}$ mode power
      transmission.  Homework, due 4/13/2017 before class. 

\item Exercise E.101: Hertz vector. Homework, due 4/13/2017 before 
      class. 

\item Exercise E.103: Vector potential of two current loops.
      Homework, due 4/18/2017 before class. 

\end{enumerate}


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