\subsection*{EC-6c~~Induction - Test Coil}

\noindent OBJECTIVES: \begin{enumerate} \epind{
\item \vspace*{-.08in}To observe the {\it emf} induced in a small detecting coil by 
the varying magnetic field produced by the varying current in a separate 
large coil.
\item \vspace*{-.08in} To follow how how this {\it emf}  depends on the shape, and the frequency of
the inducing current. The computer will produce a  voltage varying with time
in the form of a triangular waveform with 
amplitude $V_{max} = 3 \ V$ and a frequency $f = 10 \ Hz$.   
} 
\end{enumerate}

\begin{figure}[h] \centering 
\latex{\includegraphics[height=4.0cm]{figs/l104/fec6c-1.eps}}
\html{\includegraphics[height=4.0cm]{figs/l104/fec6c-1.eps}}
\vspace*{-.05in}
\caption{The triangular waveform}
\end{figure}

\noindent INTRODUCTION: \latex{\vspace*{.05in}}   \\
\pind{
The applied voltage varies linearly from $V_{min} = -3 \ V$ to
$V_{max} = 3 \ V$  in $50 \ ms$. The {\em{slope}} of the voltage curve is
therefore $\Delta V / \Delta t = 120 \ V/s$. \\
The resistance of the large coil is $R \simeq 7 \Omega$ so 
current flowing in the large coil will  vary linearly from 
$I_{min} = -3/7=-0.43 \ A$ to $I_{max} =3/7 = +0.43 \ A$ in $50 \ ms$,
 Correspondingly
$\Delta I / \Delta t = 17.2 \ A/s$.
The strength of the magnetic field produced by the
large coil 
is proportional the the voltage applied on it, and therefore
the rate of change $\Delta B/ \Delta t$ is proportional to the {\em{slope}} of
the curve that shows the voltage versus time. }\smallskip

\hspace*{.3in} \framebox[5.2in]{\parbox[b]{5in}{\smallskip {\em YOU NEED TO
KNOW:} The {\it emf} induced in  
a coil is then  
${\cal E} = -NA \Delta B/ \Delta t$  
where N is the number of turns in the small coil and 
A its cross-sectional area.   \smallskip
}}\smallskip 



\noindent EQUIPMENT: \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[$\Rightarrow$]\vspace*{-.08in} PC and interface.  
\item[$\Rightarrow$]\vspace*{-.08in} A computer controlled power amplifier.  
\item[$\Rightarrow$]\vspace*{-.08in} A stand holding a small detecting coil.  
\item[$\Rightarrow$]\vspace*{-.08in} A large coil with an ohmic resistance $R = 7 \Omega$. 
 The radius of the coil is
$r=0.1$~m. 
}
\end{enumerate}

\noindent  PROCEDURE I: (10 min) \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[1.]\vspace*{-.05in} Click on the Launch EC-6C icon below (web version) to initiate
PASCO software window.
The monitor should now show a scope window, and a window 
 for the control of the signal generator;
 CLK on the frequency, backspace and enter a 
frequency of 10 Hz. CLK on the triangular waveform. DCLK anywhere on the 
face of the scope and enter 1 V for the trigger level.
\item[2.]\vspace*{-.05in} CLK on the amplitude, backspace and enter 3 V.
\item[3.]\vspace*{-.05in} Turn on the signal generator by CLKing on the ON button then
DCLK on RECORD, you now see the voltage induced in the small coil
together with the one applied on the large coil
\item[4.]\vspace*{-.05in}  Adjust the size of the waves you see in the scope window
 using the size controls on the side of the scope window, then 
measure the height $h_1$ 
of the square wave using the cursor (5). Record this height.
}
\end{enumerate}

%\vfill \eject

\begin{figure}[h] \centering 
\latex{\includegraphics[height=3.5in]{figs/l104/fec6c-2.eps}}
\html{\includegraphics[height=3.5in]{figs/l104/fec6c-2.eps}}
%\vspace*{-.05in}
%\caption{The triangular waveform}
\end{figure}

\indent QUESTIONS    \latex{\vspace*{-.03in}}  
\begin{enumerate}
\epind{
\item[1.]\vspace*{-.05in} Explain why the induced voltage is a square wave.
\item[2.]\vspace*{-.05in} Observe the direction of the winding in the large coil. 
What is the direction of the magnetic field during the rising part
of the triangular wave? Explain your thoughts.
\item[3.]\vspace*{-.05in} Observe the direction of the winding in the small coil. 
What is the direction of the induced emf during the rising part
of the triangular wave? Explain your thoughts.
}
\end{enumerate}

\noindent  PROCEDURE II:  \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[] Move the small detecting coil 5 centimeters away from the 
large coil, measure the amplitude of the induced voltage. Repeat at distances
of 10 and 20 centimeters. Plot a graph.
}
\end{enumerate}

\indent QUESTION  \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[]\vspace*{-.05in} How does the strength of the magnetic field depend on distance?
$\sim 1/r$ ?$\sim 1/r^2$ ?$\sim 1/r^3$ ?
}
\end{enumerate}

\noindent  PROCEDURE III:  \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[1.]\vspace*{-.05in} Replace the detecting coil to its original position at the center of
the large coil. Decrease the amplitude of the triangular wave to 2 V. 
\item[2.]\vspace*{-.05in} Measure the height of the square wave. record this value.
}
\end{enumerate}

\indent QUESTIONS  \latex{\vspace*{-.03in}}  
\begin{enumerate}
\epind{
\item[Q1]\vspace*{-.05in} Did the slope of the triangular wave change? By how much?
\item[Q2]\vspace*{-.05in} Is the change in amplitude of the square wave what you would
expect? Why?
}
\end{enumerate}

\noindent  PROCEDURE IV:  \latex{\vspace*{-.03in}}  
\begin{enumerate}
\epind{
\item[1.]\vspace*{-.05in} Repeat procedure III with a frequency of 15 Hz.
\item[2.]\vspace*{-.05in} Compare the result with those of procedure I and III 
}
\end{enumerate}

\noindent  PROCEDURE V:  \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item [1.]\vspace*{-.05in} Loosen slightly the clamp holding the small coil; rotate the coil
$90^\circ$ so that it is in the horizontal plane. Observe the resulting induced
voltage.
\item [2.]\vspace*{-.05in} Rotate the coil another   
$90^\circ$ so that it is in the vertical plane again. Observe the resulting 
induced voltage. Compare the result with procedure III.
}
\end{enumerate}
