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{\bf 29:28 Physics II\\
     Spring 2005\\
     First Hour Exam \ldots February 18, 2005}\\
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Write legibly.  Start each question on a new page.  It allows me to make comments and generally keeps me in a better mood. Clearly describe what you are trying to do; it can help for partial credit. There are 5 questions.  Notice the table of fundamental constants attached to the exam.   Good luck and no whining.
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{\bf Walk with Ursus!!!}
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\noindent
{\bf (1)} Charge 1 is stuck (not free to move) and has a charge of $5 \mu C$ ($1 \mu C = 10^{-6}$ Coulombs).  Charge 2 is free to move and has a charge of $-3 \mu C$,  and a mass of 30 grams (the mass of a portion of {\em Wheaties}).  The charges are located 20 centimeters apart.     \\
(a) What is the force between them?  Be sure and say whether it is attractive or repulsive. \\
(b) Charge 2 is released from rest.  It moves 10 cm from its original position.  What is the distance between Charge 1 and Charge 2 now,  and how fast is Charge 2 moving?\\  

\noindent
{\bf (2)}  A charge $q_1 = 5 \times 10^{-6}$ C is located at coordinates $(x,y,z)=(0,5,0)$ (distances in centimeters).  A second charge $q_2= 3 \times 10^{-6}$ is located at $(x,y,z) = (0,-5,0)$.  What is the vector electric field at a point $P$ with coordinates $(x,y,z) = (10,0,0)$ ?     \\

\noindent
{\bf (3)} See Figure 1 below.      \\
(a) What is the value of $\epsilon_0 \oint \vec{E} \cdot \vec{dA}$ for contour {\bf A} (contour taken as the intersection of a closed surface with the plane of the paper)?  \\
(b)  What is the value of $\epsilon_0 \oint \vec{E} \cdot \vec{dA}$ for contour {\bf B}?\\
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\caption{Closed surfaces {\bf A} and {\bf B} surrounding charges}
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\noindent
{\bf (4)} A wire 4.0 m long and 6.0mm in diameter has a resistance of 15 m$\Omega$.  A potential of 23 V is applied across the ends of the wire.         \\
(a) What is the current in the wire?  \\
(b) Calculate the resistivity of the wire material. \\

\noindent
{\bf (5)} A charged particle with charge $q$ (positive) and mass $m$ moves in one dimension (spatial coordinate $x$) in a potential given by 
\begin{equation}
V(x) = V_0 \left( \sin(k|x|) -1 \right) 
\end{equation}   \\
(a) Draw the potential energy of the particle as a function of $x$. \\
(b) Assume that the particle is released at $x=0$ with a speed 
\begin{equation}
v = \sqrt \frac{2 q V_0}{3 m}
\end{equation}
At what point (distance from the origin) will it be turned around?  




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