\section{EC-7 Magnetism}\label{ec07_magnetism}
\subsection{EC-7a~~Lenz's Law}

\noindent OBJECTIVES: 
\begin{enumerate}
\item \latex{\vspace*{-.08in}}To observe the eddy currents induced by the magnetic field in a moving conductor.
\item \latex{\vspace*{-.08in}}To follow how the eddy current intensity depends on the shape of the conductor. \smallskip

\begin{tabular}{|p{5.2in}|}
\hline  {{\html \bf}
{\em YOU NEED TO KNOW:} 
You must understand and be able to use the Right Hand Rule in order to determine the direction and sense of the forces involved.}\\ 
\hline 
\end{tabular}
\end{enumerate}

\noindent
APPARATUS:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}} A Permanent Magnet; four different paddle pendulums;  two small red and green magnets. (There is only a single one of these set-ups per room and so, if it is in use, proceed to the next section first.)
\begin{figure}[h] \centering 
\latex{\includegraphics[height=6.5cm]{figs/l104/ec7_fig1rev.eps}}
\html{\includegraphics[height=7cm]{figs/l104/ec7_fig1rev.eps}}
\latex{\vspace*{-.08in}}
\caption {The magnet and the paddle pendulum.}
\latex{\vspace*{-.08in}}
\end{figure}
\end{enumerate}

\noindent PROCEDURE I:  (10 min)

\html{
\begin{rawhtml} 
<table width="750"> <tr><td width=375> 
\end{rawhtml}
}
\latex{\parbox{0.55\linewidth}}
{\begin{enumerate}
\item \latex{\vspace*{-.08in}} Using one of the small magnets determine the direction of the magnetic field between the jaws of the permanent magnet.
\item \latex{\vspace*{-.08in}} Observe and describe the behavior of the four pendulums when dropped between the jaws of the permanent magnet.
\item \latex{\vspace*{-.08in}} Reverse the magnet. Observe and describe the behavior of two pendulums when dropped between the jaws of the permanent magnet.
\item \latex{\vspace*{-.08in}} Set pendulum \#1 between the jaws of the magnet. Move the magnet rapidly in a direction parallel to the pendulum plate (i.e.~{\em without touching} jaws). Describe what happens.
\end{enumerate}
}
\html{
\begin{rawhtml} 
</td><td>
\end{rawhtml}
}
\latex{\parbox{0.45\linewidth}}
{
%\begin{figure}[h] \centering 
\latex{\includegraphics[height=5.5cm]{figs/l104/fec6a-2rev.eps}}
\html{\includegraphics[height=7cm]{figs/l104/fec6a-2rev.eps}} 
\begin{center}
 Figure 2: Paddle moves in the $+y$ direction
 \end{center} 
\latex{\vspace*{-.08in}}
%\caption{The setup}
%\end{figure}
}
\html{
\begin{rawhtml} 
</td></table>
\end{rawhtml}
}

\setcounter{figure}{2}

%\newpage

\noindent QUESTIONS:   
\begin{enumerate} 
\item[Q1:] \latex{\vspace*{-.08in}} Use the right hand rule to determine the motion of electrons at the moment when pendulum \#~4 enters the magnetic field  region. Is it from A to B? Or from B to A? 
\item[Q2:] \latex{\vspace*{-.08in}}What is the direction of the current flowing in the pendulum? Is it from A to B? Or from B to A?
\item[Q3:] \latex{\vspace*{-.08in}}Use the right hand rule to determine the direction of the force exerted on the current that flows in the arm of the pendulum by the magnetic field. Is it along the positive or the negative y axis?
\end{enumerate}

\subsection{EC-7b~~Induction - Dropping Magnet}

\noindent OBJECTIVE: 
\begin{enumerate} 
\item[] \latex{\vspace*{-.07in}}To show that a moving magnet induces an {\it emf} within a coil of wire. 
\end{enumerate}
 
\noindent INTRODUCTION: 
\begin{enumerate} 
\item[] \latex{\vspace*{-.08in}}After discovering the phenomenon of induction using two coils wrapped around an iron ring, Faraday was able to show that plunging a magnet into a coil of wire also generated a momentary induced current. Faraday did not use the concept of {\em{Changing Flux}} instead he thought of the {\em{`lines of force'}}, and concluded that when these lines move across a wire an {\it emf} is induced. Can you see the correspondence of this concept with the concept of flux? Think about this.
\begin{figure}[h] \centering 
\latex{\includegraphics[height=5.5cm]{figs/l104/fec6b-1.eps} \\}
\html{\includegraphics[height=5.5cm]{figs/l104/fec6b-1.eps}}
\latex{\vspace*{-.08in}}
\caption{A moving magnet - lines move across a wire}
\latex{\vspace*{-.12in}}
\end{figure}
\end{enumerate}

\noindent EXPERIMENT:
\begin{enumerate} 
\item[] \latex{\vspace*{-.08in}}
You will  be repeating Faraday's experiment by observing the {\it emf} induced in a coil by a fast moving magnet, and you will check that the {\it emf} you observe obeys the `right hand rule'. If you have the time you can see the effect of changing the speed and the polarity of the magnet.

\begin{center}
\begin{tabular}{|p{4.5in}|} 
\hline 
{\em YOU NEED TO KNOW:} Lenz's Law and the use of the right hand rule. A varying magnetic field induces a current that opposes the magnetic field change.  \\ \hline
\end{tabular}
\end{center}
\end{enumerate}

\noindent EQUIPMENT:
\begin{itemize}
\item \latex{\vspace*{-.08in}} PC, PASCO interface and power amplifier module. 
\item \latex{\vspace*{-.08in}} A voltage sensor is connected to the coil and to port A of the interface. Be sure the red wire is connected to the top of the coil. In this way a positive voltage corresponds to a current in the direction of the arrow on the top of the coil.
\item \latex{\vspace*{-.08in}} A stand holding a plastic tube and a coil. 
\item \latex{\vspace*{-.08in}} A long bar magnet, this magnet has a small cut at one end, that is the North pole.
\item \latex{\vspace*{-.08in}} A pair of red and green bar magnets 
\end{itemize}
\html{
\begin{rawhtml}  
<IMG SRC="../gif/caution.gif" ALIGN=center>  
\end{rawhtml}}
\begin{center}
\begin{tabular}{|p{4.5in}|} 
\hline
PRECAUTIONS:  The long bar magnet is very fragile!  
DO NOT DROP IT ON THE FLOOR!\\ 
In addition do not move the pair of red and green magnets any where near the permanent magnet used in EC-7a as this may flip the polarity (North-South) of these magnets.   \\
\hline
\end{tabular}
\end{center}
\html{
\begin{rawhtml} 
<IMG SRC="../gif/caution.gif" ALIGN=center>  
\end{rawhtml}
}

\noindent  PROCEDURE I: (15 min)
\begin{enumerate}
\item \latex{\vspace*{-.08in}} Click on the Launch EC-7B icon below (web version) to initiate the PASCO software window.
\input{toolbar/ec7_tb1}
\item \latex{\vspace*{-.05in}} Set  the distance $d_1 \sim 15 \ cm$ between the  top of the plastic tube and the top of the coil. Record this in your lab notebook. Be sure that the red terminal of  the voltage sensor is plugged
on the top plug of the coil.
% Check the 
%polarity of this end using the  colored bar magnets.
%\vfill \eject 
\end{enumerate}
\noindent
\latex{\vspace*{-.05in}}

\html{
\begin{rawhtml} 
<table width="750"> <tr><td width=50%> 
\end{rawhtml}
}
\latex{\parbox{0.5\linewidth}}
{\begin{enumerate}
\item[3.] \latex{\vspace*{-.08in}} The long bar magnet has a narrow cut at one end, this is the North pole of the magnet.
\item[4.] \latex{\vspace*{-.08in}} Hold the long bar magnet at the top of the tube; the end with the cut should be down, and just one centimeter or so inside the tube.
\item[5.] \latex{\vspace*{-.08in}} CLICK on the START icon and drop the magnet immediately afterwards.
\item[6.] \latex{\vspace*{-.08in}} to see the whole graph, and measure the heights $h_1$ and $h_2$ of the two peaks using the cursor cross-hairs (5).
\item[7.] \latex{\vspace*{-.08in}} Slide the tube upwards, remove the rubber stopper and the magnet, replace the rubber stopper at the bottom of the plastic 
tube, and slide the tube down again.
\item[8.] \latex{\vspace*{-.08in}} Print the graph on printer.
\end{enumerate}
}
\html{
\begin{rawhtml} 
</td><td> 
\end{rawhtml}
}
\latex{\hspace*{.03in}\parbox{0.5\linewidth}}
{
%\begin{figure}[h] \centering 
\latex{\includegraphics[height=8.5cm]{figs/l104/fec6b-2rev.eps}}
\html{\includegraphics[height=8cm]{figs/l104/fec6b-2rev.eps}}
\begin{center}
Figure 4: The setup
\end{center}
\latex{\vspace*{-.08in}}
%\caption{The setup}
%\end{figure}
}
\html{
\begin{rawhtml} 
</td></table>
\end{rawhtml}
}
\setcounter{figure}{4}

\noindent QUESTIONS: (10 min) 
\begin{enumerate}
\item[Q1:] \latex{\vspace*{-.08in}} The graph you obtained has a fall, a rise, a very short flat part, then a rise and finally a fall. Explain what is happening at these various  times.
\item[Q2:] \latex{\vspace*{-.06in}} Explain why the two voltage peaks you measured in 1.6 are not the same size. Can you give an approximately quantitative justification for the ratio $h_1/h_2$?
\item[Q3:] \latex{\vspace*{-.06in}} Examine the direction of the winding in the coil; verify that the directions of the peaks is what you would expect using the right hand rule (curled fingers = current;~~~thumb = magnetic field).
\end{enumerate}

\noindent PROCEDURE II: (10 min) 
\begin{enumerate}
\item[] \latex{\vspace*{-.08in}} Repeat procedure I with the magnet inverted (the South Pole at the bottom). 

\item[] \latex{\vspace*{-.03in}}QUESTION: 
\begin{enumerate}
\item[Q1] \latex{\vspace*{-.07in}} Explain in what way(s) and why the new graph is different.
\end{enumerate}
\end{enumerate}

\noindent PROCEDURE III: (20 min) 
\begin{enumerate}
\item \latex{\vspace*{-.05in}} Move the coil further down on the tube making the new distance $d_2$ at least about two and a half  times larger than $d_1$. Record this new distance $d_2$.  
\item \latex{\vspace*{-.05in}} Repeat procedure I. Measure and record the heights $h^\prime _1$ and $h^\prime _2$ of the new peaks.
 

\item[] \latex{\vspace*{-.05in}}QUESTIONS: 
\begin{enumerate}
\item[Q1] \latex{\vspace*{-.08in}} Explain the reason for the difference between this graph, and the one obtained in procedure I.
\item [Q2] \latex{\vspace*{-.08in}} Can you give an approximate quantitative explanation for the ratio $h^\prime _1 / h_1$? HINT: remember Newtonian mechanics formula for free fall $v=\sqrt{2gh}$ where $g$ is the acceleration due to gravity .
\end{enumerate}

\end{enumerate}

\subsection{EC-7c~~Induction - Test Coil}

\noindent OBJECTIVES: \begin{enumerate} 
\item \latex{\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 \latex{\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 $f = 10 \ Hz$.   
 
\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}
\end{enumerate}

\noindent INTRODUCTION:
\begin{enumerate} 
\item \latex{\vspace*{-.08in}}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
\begin{center}
\begin{tabular}{|p{4.5in}|} 
\hline 
{\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. \\
\hline
\end{tabular}
\end{center}
\end{enumerate}

\noindent EQUIPMENT:
\begin{itemize}
\item \latex{\vspace*{-.1in}} PC and PASCO CI-750 interface.  
\item \latex{\vspace*{-.1in}} Power amplifier module. 
\item \latex{\vspace*{-.1in}} A stand holding a small detecting coil.  
\item \latex{\vspace*{-.1in}} Two large back-to-back coils with an ohmic resistance $R = 7 \Omega$. The radius of the coil pair is $r=0.1$~m.  The {\em output} signal from the PASCO goes to the {\em input} of the Power Amp and then the output from the Power Amp
goes to the large coil (using the RED and BLACK banana jacks).  
\end{itemize}

\noindent  PROCEDURE I: (10 min) 
\begin{enumerate}
\item \latex{\vspace*{-.08in}} Click on the Launch EC-7C 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. If necessary set the frequency to 10 Hz and the pull down menu to choose the triangular (or sawtooth) waveform.  In the oscilloscope window set the trigger level to 1 V.
\input{toolbar/ec7_tb2}
\item \latex{\vspace*{-.08in}} If necessary adjust the signal generator amplitude to  3 V.
\item \latex{\vspace*{-.08in}} Analog channels A and B are used to sense the voltage drop across the large coil (A) and the
voltage induced in the small coil (B).  Connect the banana jack wires RED to RED and BLACK to BLACK..
\item \latex{\vspace*{-.08in}} Turn on the signal generator by CLICKing on the ON button then initiate data acquisiton by CLICKing on the START icon.  You should now see the voltage induced in the small coil together with the one applied to the large coil.
\item \latex{\vspace*{-.08in}}  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.
%\vfill \eject

\begin{figure}[h] \centering 
\latex{\includegraphics[height=3.4in]{figs/l104/fec6c-2rev.eps}}
\html{\includegraphics[height=3.5in]{figs/l104/fec6c-2rev.eps}}
\vspace*{-.05in}
\caption{The layout with the Pasco CI and back-to-back coil assembly.}
\end{figure}
\end{enumerate}
\setcounter{figure}{6}
\begin{enumerate}
\item[] QUESTIONS
\begin{enumerate}
\item \latex{\vspace*{-.05in}} Explain why the induced voltage is a square wave.
\item \latex{\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 \latex{\vspace*{-.05in}} Observe the direction of the winding in the small coil. What is the direction of the induced {\it emf} during the rising part of the triangular wave? Explain your thoughts.
\end{enumerate}
\end{enumerate}

\noindent  PROCEDURE II:
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}}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. Make a simple graph using Microsoft Excel or any other suitable application.
\end{enumerate}

\begin{enumerate}
\item[] \latex{\vspace*{-.08in}}  QUESTION 
\begin{enumerate}
\item[] \latex{\vspace*{-.08in}} How does the strength of the magnetic field depend on distance? $\sim 1/r$ ?$\sim 1/r^2$? $\sim 1/r^3$? \latex{\vspace*{-.05in}}
\end{enumerate}
\end{enumerate}

\noindent  PROCEDURE III:
\begin{enumerate}
\item \latex{\vspace*{-.08in}} 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 \latex{\vspace*{-.08in}} Measure the height of the square wave and record this value.
%\end{enumerate}

\item[] \latex{\vspace*{-.07in}}QUESTIONS
\begin{enumerate}
\item[Q1:] \latex{\vspace*{-.08in}} Did the slope of the triangular wave change? By how much?
\item[Q2:] \latex{\vspace*{-.08in}} Is the change in amplitude of the square wave what you would expect? Why?
\end{enumerate}
\end{enumerate}

\noindent  PROCEDURE IV: 
\begin{enumerate}
\item \latex{\vspace*{-.08in}}Repeat procedure III with a frequency of 15 Hz.
\item \latex{\vspace*{-.08in}}Compare the result with those of procedure I and III 
\end{enumerate}

\noindent  PROCEDURE V: 
\begin{enumerate}
\item[1.] \latex{\vspace*{-.08in}} 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.] \latex{\vspace*{-.08in}} 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}

\subsection{EC-7d~~Induction - Faraday Discovery}

\noindent INTRODUCTION: 
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}
Michael Faraday (1791-1867) was a bookbinder journeyman (English for apprentice). He read some of the books he was supposed to bind, and became interested in `natural philosophy' (the term science did  not exist in the XVIII$^{th}$ century). \\
In 1813 he applied for a job as a technician in the laboratories of the Royal Laboratories to professor Davy, he got the job. Some people say that this was the greatest discovery Davy ever made! He worked all his life in the laboratories, starting as a technician,  became Director of the Laboratories, was elected to The Royal Society of London, and became a Professor at the Royal Institution. Some of you will be pleased to know that he knew no math, and never used math in his researches.

Faraday performed many kinds of experiments, in chemistry, optics, and metallurgy, but perhaps the most important experiments were on electricity and magnetism. Having learned of Oersted's experiments on the magnetic fields produced by an electric current, he wondered if the reverse could be true: perhaps magnetic fields could in turn produce an electric current. His first experiments were unsuccessful, until he realized that it was the {\em change} in magnetic field that produced a {\em momentary} current. 
 
His first experiments were similar to the one you will be doing today: two separate coils were wound on an iron ring, the current in the primary coil was interrupted, and the momentary current in the secondary was observed. 

The explanation of this effect is, as you know, that the change in current in the primary circuit produces a change in the magnetic field that exists inside the secondary coil, the electromotive force in the induced secondary is then $${\cal E} = -AN \cdot(\Delta B/\Delta t)$$
where $N$ is the number of turns, and $A$ is the cross-sectional area of the secondary coil.
\end{enumerate}


\noindent OBJECTIVES:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}To observe the induced momentary {\it emf} that appears in a secondary circuit when the current in the primary circuit is turned on, or interrupted. This
is the original Faraday discovery: induction of a current by a varying magnetic field.

\begin{figure}[h] \centering 
\latex{\includegraphics[height=4.0cm]{figs/l104/fec6d-1.eps}}
\html{\includegraphics[height=4.0cm]{figs/l104/fec6d-1.eps}}
\latex{\vspace*{-.05in}}
\caption{Faraday's experiment}
\end{figure}

In procedure II you will observe that induced momentary emf appears 
also in the primary circuit itself when the current is turned on, or interrupted; you will be observing the self induction of a coil.  Faraday used a switch to interrupt or start the current as shown in Fig~1;  you will use the computer to do the same job: the computer will produce a square wave, the voltage will change abruptly from 0 volts (current off = switch open) to a value of about 4 Volts (current on = switch closed) as shown below.
\begin{figure}[h] \centering 
\latex{\includegraphics[height=3.0cm]{figs/l104/fec6d-2.eps}}
\html{\includegraphics[height=3.0cm]{figs/l104/fec6d-2.eps}}
\latex{\vspace*{-.05in}}
\caption{The square wave}
\latex{\vspace*{-.1in}}
\end{figure}
\end{enumerate}

\noindent EQUIPMENT:
\begin{itemize}
\item \latex{\vspace*{-.08in}} PC and PASCO CI-750 interface, again with Output connect to the power amplifier input. 
\item \latex{\vspace*{-.08in}} Two voltage sensors are plugged in the interface. The voltage sensor plugged in the A port measures the voltage across the external resistor;  the voltage sensor plugged in the B port measures the voltage across the coil.
\item \latex{\vspace*{-.1in}} Computer controlled Power Amplifier Module.  
\item \latex{\vspace*{-.1in}} A pair of nested coils. The outer  one is the `primary'.  It  has about 2600 turns of fine wire and has a resistance of $\sim 95~\Omega$. The primary coil is insulated from the inner secondary coil, an iron bar fits inside 
the inner coil.   
\item \latex{\vspace*{-.1in}} A plug board and a $100~\Omega$ resistor. 
\end{itemize}


\noindent  PROCEDURE I:
\begin{enumerate}
\item \latex{\vspace*{-.06in}} Click on the Launch EC-7D icon below (web version) to initiate the PASCO DataStudio software window.
\input{toolbar/ec7_tb3}
\item \latex{\vspace*{-.06in}} Check that the power amplifier is on, (the yellow pilot light labeled `Power' should be on and the red pilot light light labeled `Distorting' on the power amplifier should off).
\item \latex{\vspace*{-.06in}} Check that the amplitude is $\sim$ 4 Volts, and the frequency is $\sim$ 10 Hz. CLICK on the ON button of the Signal Generator, then CLICK on START icon.  The CLICK on STOP after a second or so.
\latex{\vspace*{-.15in}}
\begin{figure}[h] \centering 
\latex{\includegraphics[height=7.0cm]{figs/l104/fec6d-3rev.eps}}
\html{\includegraphics[height=7.0cm]{figs/l104/fec6d-3rev.eps}}
\latex{\vspace*{-.05in}}
\caption{The schematic setup}
\end{figure}
\begin{figure}[h] \centering 
\latex{\includegraphics[height=5.0cm]{figs/l104/fec6d-4.eps}}
\html{\includegraphics[height=5.0cm]{figs/l104/fec6d-4.eps}}
\latex{\vspace*{-.05in}}
\caption{The physical setup}
\end{figure}
\item \latex{\vspace*{-.05in}} The computer monitor should now display two curves:  \\
- one curve (curve A) looks like a square wave, but not quite; it shows the voltage across the external $100 \ \Omega$ resistor, and therefore tells you the current flowing in the coil. \\
-the other curve (curve B) shows the induced voltage across the secondary coil
\item \latex{\vspace*{-.06in}} CLICK on GRAPH SETUP (8) then print the graph of one of the peaks [instructions in  \hyperref{PASCO Interface and Computer Primer}{PASCO Interface and Computer Primer section (refer to Appendix~}{)}{PASCO}]

\item[]  \latex{\vspace*{-.05in}}QUESTIONS:   
\begin{enumerate}
\item[Q1:] \latex{\vspace*{-.07in}} The shape of curve A is not quite a `square wave'. Why not? HINT: this is an LR circuit with a time constant $\tau = L/R$
\item[Q2:] \latex{\vspace*{-.07in}} Are the peaks of voltage across the secondary coil, (curve B) that correspond to current on vs.\ current off 
about the same size? Explain.
\item[Q3:] \latex{\vspace*{-.07in}} Are the peaks of voltage across the secondary coil, that correspond to current on vs. current off of the same polarity? Explain.
\end{enumerate}
\end{enumerate}

\noindent PROCEDURE II: (15 min)
\begin{enumerate}
\item \latex{\vspace*{-.05in}}Remove the voltage sensor banana pins from the terminals  R and S of the secondary coil and insert them into the terminals P and Q of the primary coil,  without disconnecting these terminals from the power supply. 
\item \latex{\vspace*{-.05in}}CLICK on the ON button of the Signal Generator, then DCLICK on START, DCLICK on STOP after a second.
\item \latex{\vspace*{-.05in}}The Monitor now displays two curves:  \\
- one curve (curve A) looks like a square wave, but not quite; it shows the voltage across the external $100~\Omega$ resistor, and therefore tells you how the current flowing through the primary coil varies with time. \\
-the other curve (curve B) shows the voltage across the primary coil.  \\
The two curves look very similar: they should have about the same height, and
should rise and fall at the same times.

If curve B is inverted relative to curve A, exchange the banana pins in terminals P and Q and repeat item 1.2 of this procedure.
\item \latex{\vspace*{-.05in}}CLK on GRAPH SETUP (8) then print the graph of one of the peaks  [instructions in  \hyperref{PASCO Interface and Computer Primer}{PASCO Interface and Computer Primer section (refer to Appendix~}{)}{PASCO}]

\item[] QUESTIONS 
\begin{enumerate} 
\item[Q1:] \latex{\vspace*{-.08in}} The shape of curve A is not quite a `square wave', why not? HINT: this is an LR circuit with a time constant $\tau = L/R$
\item[Q2:] \latex{\vspace*{-.08in}} The curve that describes the voltage across the primary coil, (curve B) is similar to curve A. Why? HINT: think of two approximately equal
resistors in series.
\item[Q3:] \latex{\vspace*{-.08in}} The curve that describes the voltage across the primary coil, (curve B) is similar to curve A, but it shows `spikes'. Why? HINT: the voltage across this coil is due to two factors, R and L.
\end{enumerate}
\end{enumerate}
