\section{E7U. (6) Electromagnetic Induction}\label{e07_induction}


%\subsection{Relevant Physics Theory}
%*** Place here some text and at least one diagram. 
%This text can describe magnetic induction as in the 
%208 text books and 208 classwork. 
%It should be sufficient for the rare cases in which the experiment is done 
%before the classwork.The diagram should clearly show the direction of an induced emf. 
%Be careful with notation and defn of emf. ***

\noindent OBJECTIVE: \vspace*{.1in} \\
\begin{mp1}To study electromagnetic induction and  verify both Lenz's law and Faraday's law.\\
\end{mp1}

\indent Preliminary Questions:
\begin{enumerate} \epind{
\item When you are looking along the axis towards a circular coil,  a current is present moving in a clockwise direction. (This means that the apparent movement of positive changes is clockwise and the movement of the negative electrons is anticlockwise.)

In what direction is the magnetic field at the center of the coil? 
(Towards you or away from you?)
\item
Does an unchanging magnetic field cause an induced voltage in any circuit?
\item
Describe two common items in your house or car whose operation relies upon 
``Electromagnetic Induction''.
\item
If the magnetic flux through a circuit changes at twice the rate, 
does it cause the induced voltage to be doubled, halved or multiplied by $\sqrt{2}$?
}\end{enumerate}
\subsection{Demonstration}
\begin{itemize}
\item A strong permanent magnet with a gap of about 100 mm, a coil of wire and a 
medium impedance moving coil voltmeter. The magnetic poles are labelled N and S. 
The voltmeter inputs are labelled `current in'' and ``current out''.

Use this simple system to verify the direction of the emf ${\cal E}$ which is induced 
when the coil is moved into the magnetic field.
\item
An AC generator which can be turned by hand with a DC voltmeter to see the 
output voltage varying with time. This illustrates the significance of the magnetic induction 
which will be measured in this experiment. Notice that the voltages are increased by 
changing, more quickly, the magnetic field through the coils of wire. In fact, Faraday's law predicts 
that the emf ${\cal E}$, which is induced in coils of contant area, is proportional to 
$\frac{\partial \Phi}{dt}$ where $\Phi$ is the magnetic flux through the circuit. 
The electrical power which is delivered to us all depends upon magnetic induction.

Industrial electrical generators, such as those at Madison Gas and Electric,  have iron
cores to greatly 
increase the magnetic field and the voltages which are induced by its changes. 
However, the iron cannot be everywhere in a system of moving coils since some clearance
must be left for insulation and between the moving parts.
In a system with iron in only some places, the field $\vec{B}$ and rate of change 
$\frac{d\vec{B}}{dt}$ are hard to calculate. 

For that reason, in this experiment, we will 
avoid the use of iron and measure some smaller but predictable voltages.
\end{itemize}

%\subsection{Preliminary Questions}
%\begin{enumerate}
%\item ?
%\item ?
%\item ?
%\item ?
%\end{enumerate}

\subsection{APPARATUS}
\begin{itemize}  
\item Three coil Systems;\\
--one primary pair of large Helmholtz Coils, \\
--two similar many-turn secondary coils;\\
\item a computer with an internal plug-in board with Analog-to-Digital-Conversion (ADC) to give
the ability to measure voltages; \\
\item a high impedance digital voltmeter; \\
\item a dry battery with a 100k ohm resistor in series and the  positive terminal colored red 
with a large ``{\Large +}'';\\ 
\item permanent rod magnet with its North Magnetic pole marked in red and with a ``{\Large N}'';\\
\item brass and iron rods; \\
\item Ramping Current supply; \\
\item small compass with the North Magnetic Pole marked with luminous paint; \\
\item the Earth with\\
-- the Geographic North Pole and a South Magnetic Pole near it but deep under 
   upper Canada and also \\
-- the Geographic South Pole with a North Magnetic Pole near it but deep under 
   the Antarctic Plateau.\\
\item (optional:  model generator/motor).
\end{itemize}

\noindent {\bf CAUTION}    If a strong magnet has been placed close above or below the 
compass needle, 
the needle may have remagnetized to the opposite polarity.

In this experiment, we will use a pair of Helmholtz Coils as the ``primary''. 
The Helmholtz Coils of radius $R$ are 
placed a distance $R$ apart on the same axis and the Coils are connected in series so 
that the current flows in the same way (clockwise or anticlockwise) in both coils. 
This particular configuration, of radius = distance apart, is often used
to give a very uniform magnetic field in the central region.

\subsection{Why use a Computer?}
In this experiment, a computer is very helpful for 3 reasons.
\begin{enumerate}
\item  It can record voltages very quickly during the change of the magnetic field. 
It would be impossible for a person to record 10 or more voltages during a change lasting 2 seconds.
\item It can meaure voltages more precisely than a person can read a ordinary meter.
\item It can sum thousands of results to calculate an integral with respect to time.
\end{enumerate}
\subsection{INVESTIGATIONS OF LENZ'S LAW}
Reminder: ``An induced current in a closed conducting loop will appear in such a direction
that it opposes the change that produced it.''

 Procedure:
Verify the direction of the induced emf ${\cal E}$ in the secondary Coil due to several procedures.
\begin{enumerate}
\item {Initial Set-up of Apparatus}\\
Set up the secondary circuit with 2 jumper cables twisted together and loosely connecting 
the 4800 turn winding of the secondary coil (ie n=4800) to the terminals on the base. 
Connect these, in turn, to the computer ADC input terminals. \\
Set the computer to read 2 kSample/second ...\\
Set the Range Configuration to be ``-10 V to + 10 V'' so that both positive and 
negative voltages can be read.\\
Set the gain to be 100.0 so that each Least Count of the ADC corresponds to 
a voltage input of 3.0518 microvolts.


\item Move the magnet so that the magnetic field enters the secondary coil from the right
(ie bring the magnet North pole  closest to the right side of the secondary coil).\\
        --Is the emf induced clockwise or anticlockwise in the secondary as seen along the axis 
        from the right?\\
        --If a small resistor was connected across the terminals of the secondary,
        so that a current surge could flow in the secondary during the movement then, in which direction 
        would the secondary 
        experience a force due to this current surge and the magnetic field of the magnet?
        (In this setup, the force is too small for you to feel but, if you can predict the 
        direction of the force.)\\
        --In which direction would Lenz's Law predict the force?
\item Move the magnet so that its magnetic field $B$ enters the secondary coil from the left
(ie bring the magnet North pole  closest to the left side of the secondary coil).\\
        --Is the emf ${\cal E}$ induced clockwise or anticlockwise in the secondary as seen along the axis 
        from the right?\\
        --If a small resistor was connected across the terminals of the secondary,
        so that a current surge could flow in the scondary during the movement, in which direction 
        would the secondary 
        experience a force due to the current surge and the magnetic field of the magnet?
\item Place the magnet in a position in which its magnetic field enters the secondary 
        coil from the right. Then remove the magnet and its field.
        During the removal, is the emf ${\cal E}$ induced clockwise or anticlockwise 
        (as seen looking along the axis from the RHS) in the secondary?
\item 
\begin{enumerate}
\item Consider the solenoidal sense coil or ``secondary coil'' already mounted within the pair of Helmholtz Coil.
        Connect the Ramping Current Supply to the Hemholtz Coils  so 
        that the current flows clockwise (seen from the right hand side) in both coils
        and causes a magnetic field along the axis from your right to left.
        Use a current of about +10 Amp. 
\item Push the transistion button on the Ramping supply and 
        notice how the current ramps down and up. It can ramp down to either zero current 
        (from +10 A to 0) or to the negative equal current (from +10 A to -10 A).
        The current is restored to +10 A when you release the pushbutton.
\item Use a compass to check the direction of the magnetic field $\vec{B}$in the 
        central region.
        Push the button to reverse the current and notice whether the field $\vec{B}$ reverses.
\item Connect, in series, another simple circuit consisting of only the dry battery, 
        a 100k ohm resistor and the galvanometer in series.
        Determine whether the current must flow from the battery ``+'' terminal
        into the red or the black banana
        socket for the galvanometer to show a positive current.
\item Connect the galvanometer across the secondary so that a clockwise  induced emf 
        ${\cal E}$ (as seen looking along the axis from the RHS)in the secondary will 
        cause the galvanometer to indicate a positive current. 
        You can do this by following the direction of the wires from the secondary's wire turns 
        to the galvanometer.
\item Push the transistion button on the Ramping Supply and notice the induced emf 
        in the secondary.
        When the primary current changes from 0 to +10 A, (in a clockwise direction seen 
        from the RHS), record the direction (Clockwise or anticlockwise seen from the RHS)
        of the induced current flow and induced emf in the secondary.\\
        In which direction does Lenz's Law predict the direction of the emf ${\cal E}$ 
        in the secondary?
        
        *** At what point should the student start using the computer to measure voltages?***

\end{enumerate}
\item Connect the dry battery and 100k ohm resistor in series with the computer's 
        voltage measuring terminals. 
        As before, determine whether the current must flow into the red or the black banana
        socket for the computer's terminals from the computer to show a positive current.
        
\item Connect the computer terminals across the secondary so that a clockwise 
        (around the axis of the secondary solenoid as seen from the RHS) 
        induced emf ${\cal E}$ in the secondary will cause the computer to indicate a positive 
        current. 
        You can do this by following the direction of the wires from the secondary's wire turns 
        to the computer.
        
\item Push the transistion button on the Ramping Supply and notice the induced emf.
        When the primary current changes from 0 to +10 A, (in a clockwise direction seen 
        from the RHS), record the direction (clockwise or anticlockwise seen from the RHS)
        of the induced current flow and induced emf in the secondary.\\
        In which direction does Lenz's Law predict the direction in the secondary?
\item ?
\item ? Put a lamp or LED across the secondary? (It can receive 5.5 mA from an 
impedance of 1.7 kohm.)
\item ?
\end{enumerate}
Write your conclusions about the directions of the induced emfs.

\subsection{INVESTIGATIONS OF FARADAY'S LAW}
First Reminder: The ``Magnetic Flux $\Phi$'' which passes through a surface, bounded by
a closed loop, measures the number of magnetic lines of force through that surface.''\\
More precisely, the ``Magnetic Flux $\Phi$'', through a surface $\vec{A}$, is the integral 
of the scalar product

$\Phi=\int \vec{B}.\vec{dA}$   ''

\vspace{10mm}

Second Reminder:``If a circuit is temporarily broken and a voltmeter is placed across 
the break, the voltmeter is said to measure the ``Electromotive Force'' or 
emf ${\cal E}$ of the rest of the circuit''.

\vspace{10mm}

Third Reminder: ``The Electromotive Force (emf) ${\cal E}$ induced in a conducting loop is equal to the 
negative of the rate at which the magnetic flux $\Phi$ through that loop is changing with time.''

${\cal E}=-\frac{d\Phi}{dt}$

Notes 
\begin{itemize}
\item If we make a conducting loop with the wire having n turns, then the magnetic field
induces an emf in each turn and so the total emf ${\cal E}$ of the n turns is n times that of each turn. 
The result is the same as if n times the flux was through a single turn.

\item We measure the voltage with a very high impedance ``voltmeter'' in the computer and so we 
can directly measure the emf ${\cal E}$ as a simple voltage.

\item The magnetic flux $\Phi=\int \vec{B}.\vec{dA}$ can be changed in several ways.\\ 
The current in a primary coil can be changed or\\
the position of a magnet or primary coil can be changed or\\
the position of the secondary coil can be changed or\\
the shape and size of the secondary coil can be changed or\\
the orientation of the secondary coil to the magnetic field can be changed.

\item We will neglect the Earth's magnetic field for 2 reasons
\begin{itemize}
\item If I is near 18 A, the field of the coil is near 2.3 millitesla while the Earth's field 
is only about 60 microtesla.
\item We are concerned with only changes in the flux through the coil and, unless the secondary 
coil is rotated, the flux due to the Earth is constant.
\end{itemize}
\end{itemize}
 
 Faraday's Law agrees with Lenz's Law but Faraday's Law gives us the \underline{magnitude} 
 of the induced 
 emf while Lenz's Law gives us \underline{direction} of the induced emf.\\
 In our experiment, we will use two alterations to make the apparaus more simple.\\
 \begin{itemize}
 \item We will use the Helmholtz Coils, instead of a magnet, to create or destroy a Magnetic 
 field because 
 \begin{itemize}
 \item the field B of a Helmholtz system is uniform and can be readily calculated whereas
 \item the field B of a magnet is nonuniform and is not easily measured.
 \end{itemize}
 \item Although in the next procedure we will test Faraday's Law 
 
 ${\cal E}=-\frac{d\Phi}{dt}$, 
 
 \noindent
 in the later procedures, we will test the integral of both sides of the equation
 
 $\int{\cal E}dt=-\Phi$
 
 We use the integral method later because the computer can easily add many measurements to integrate ${\cal E}$
 whereas it is hard to cause a precise $\frac{d\Phi}{dt}$ since it is hard to
 cause a current ramp with a precise $\frac{dI}{dt}$.
 \end{itemize}
 
 \subsection{Procedure:}
Verify the magnitude of the induced emf ${\cal E}$ in the secondary Coil due to several 
procedures.

*** This procedure assumes the use of the
{\bf National Instruments Enhanced Multifunction I/O board PCI-MIO-16XE-50 for PCI
(Natl Inst 1996 Catalog pg 3-104)}. ***
\begin{enumerate}
\item {Initial Set-up of Apparatus}\\
Retain the set up you already have for the secondary circuit.\\
Set up the primary circuit by connecting the Ramping Supply so that the current output
will cause a current to flow clockwise in the Helmholtz Coils (as seen from the RHS).
Remember that the current must flow from the supply to one big Coil then to the next
big Coil and then back to the supply.\\
Set the maximum current to 18.0 Amp by adjusting the helipot while watching the digital current scale.
(The helipot numbers have no meaning except as a fraction of the maximum current.)

\item 
To keep your notes tidy, we suggest making a short table of your results; with the headings

\noindent
\begin{tabular}{|p{12mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|}
\hline
item \# & $\Delta I$&$\frac{dI}{dt}$&$n$ & $N$ & Calculated $-\frac{d\Phi_{1}}{dt}$ 
                                        & Measured ${\cal E}_{1}$ 
                    & ratio $\frac{{\cal E}_{1}}{-\frac{d\Phi_{1}}{dt}}$\\
\hline
\hline
1 & & & & & & &\\
\hline
\end{tabular}

\begin{enumerate}
\item Set the Ramping Current Supply to have transitions from +18 A to -18 A 
($\Delta I_{1}=36\ A$) and back.
Set the transistion rate to $\pm 20\ A/s$ meaning it will take a time 
$\Delta t=\frac{\Delta I_{1}}{(\frac{\Delta I}{dt})}=\frac{36\ A}{20\ A/s}=1.8\ seconds$
 for each transition.
 \item Set the computer menus to have a full scale voltage of ?? volts

\item Calculate the rate of change of the magnetic flux $\frac{d\Phi}{dt}$ that will occur 
if the primary current is changed at a rate near $\frac{dI}{dt}=20\ A/s$.
\item
Since the magnetic field at the center of a Helmholtz Coil carrying current I 
in each of two coils with $N$ turns is 
                
                $B=\frac{\mu_{0}8}{\sqrt{125}}\frac{NI}{R}$ 
                
\noindent
The effective area of a solenoid of $n$ turns when pointing at angle $\theta$
from the magnetic field is $A=n\pi r^{2}.Cos\theta$.
Thus a change in current $\Delta I$ will create an induced emf

$\Phi=\frac{\mu_{0}8}{\sqrt{125}}.\frac{\pi r^{2}Cos\theta }{R}. Nn\delta I$ 
                

Since you will need to calculate $B$ for several cases, you might as well now calculate a
temporary useful factor $F$;

        $F=\frac{BA}{NI}=\frac{\mu_{0}8}{\sqrt{125}}.\frac{\pi r^{2}Cos\theta }{R}$
                
\noindent
Write the value of $F$ and be careful of powers of 10 and of the units.
Now you will be able to quickly calculate the change in magnetic flux due to a 
change in current

$\Delta \Phi=F. Nn\delta I$ 

\noindent
and

$\frac{d\Phi}{dt} = FNn\frac{dI}{dt}$.
                
\item Use the factor $F$ to calculate the rate of change of the magnetic flux $\frac{d\Phi}{dt}$ that will occur 
if the primary current is changed at a rate near $\frac{dI}{dt}=20\ A/s$.

\item Push the Transition button to cause the current in the primary and its magnetic field
to reverse over a time of 1.8 seconds. Note the value of the induced emf ${\cal E}_{1}$ which 
the computer records during the change. The list in the computer of values of ${\cal E}_{1}$
should start at zero, become non-zero during the flux change, then become zero after the 
flux change.
\item
Check the agreement between ${\cal E}_{1}$ and $-\frac{d\Phi_{1}}{dt}$. 
\item Release the pushbutton so that the reverse transition occurs. 
Again, check ...
\end{enumerate}
\item 
Make a larger table with at least 4 more lines and record the results of the following 
measurements.

\noindent
\begin{tabular}{|p{12mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|p{17mm}|}
\hline
item \# &$\Delta I$ &$\frac{dI}{dt}$&$n$ & $N$ & Calculated $-\Phi$ 
                                        & Measured $\int {\cal E}dt$ 
                    & ratio $\frac{\int {\cal E}dt}{-\Phi}$\\
\hline
\hline
2 & & & & & & & \\
\hline
3 & & & & & & & \\
\hline
4 & & & & & & & \\
\hline
etc & & & & & & & \\
\hline
\end{tabular}
Keep the same Current and Current Transition Rate as in item 1, 
(ie $\Delta I_{2}=\Delta I_{1}$, $n_{2}=n_{1}$, $N_{2}=N_{1}$ and 
$(\frac{dI}{dt})_{2}=(\frac{dI}{dt})_{1})$.
\begin{enumerate}
\item Calculate the magnetic flux change that will occur if the primary current is reversed.
\item Push the Transition button to cause the current in the primary and its magnetic field
to reverse over a time of 1.8 seconds. Note the values of the induced emf ${\cal E}_{2}$ which 
the computer measures.
\item Use the computer to integrate the $\int {\cal E}_{2}dt$.
\item Check the agreement between $\int {\cal E}_{2}dt$ and $-\Phi_{2}$. 
\end{enumerate}

\item Take another variation of 4 variables 
(the current change $\Delta I_{3}$, 
the number of turns $n_{3}$ in the secondary  
the number of turns $N_{3}$ in the primary) and
the rate of change of current $(\frac{dI}{dt})_{3}$. 
\begin{enumerate}
\item Calculate the expected flux change and 
\item Push the Transition button again to cause the primary's magnetic field
to reverse over a time of 1.8 seconds. Again the computer can measure the induced 
emf ${\cal E}_{3}$.
\item Integrate $\int {\cal E}_{3}dt$.
\item
Check the agreement between the third values of $\int {\cal E}_{3}dt$ and $-\Phi_{3}$. 
\end{enumerate}

\item Repeat the procedure for another variation of the 4 variables 
($\delta I$, $n$, $N$ and $(\frac{dI}{dt})$
and check the agreement between the fourth values
of $\Phi_{4}$ and $\int {\cal E}_{4}dt$

\item Reduce the Ramping Supply's $\frac{dI}{dt}$ to, say $\frac{dI}{dt}=2\ A/s$ and, 
keeping the same values of the other 3 variables in the primary as in the previous item
(ie $I_{5}=I_{4}$, $n_{5}=n_{4}$, and $N_{5}=N_{4}$), repeat the procedure 
and check the agreement between the fifth values
of $\int {\cal E}_{5}dt$ and $-\Phi_{5}$. Notice that although the values of $\int {\cal E}_{5}dt$
were smaller, the change and the integral lasted for a longer time and so $\Phi_{5}$ 
and $\int {\cal E}_{5}dt$ were not changed.

\item \begin{enumerate}
\item Set $I_{6}=18\ A$, 
\item Rotate the Secondary Coil and let the computer measure the emf ${\cal E}_{6}$
for about a rotation of 90 degrees.
\item Study the nature of the measured values of ${\cal E}_{6}$. 
\item Why would you expect the voltage to have a sinusoidal nature?
\end{enumerate}

\item \begin{enumerate}
\item Set $I_{7}=18\ A$, 
\item Rotate the Secondary Coil and let the computer measure the emf ${\cal E}_{7}$
for about 3 turns.
\item Study the nature of the measured values of ${\cal E}_{7}$. 
\item Why would you expect the voltage to have a sinusoidal nature?
\end{enumerate}

\item If you have time, try a few more choices of the 4 variables
($\Delta I$, $n$, $N$ and $(\frac{dI}{dt})$). 
In each case, calculate the expected $\Phi$, measure $\int {\cal E}dt$  compare the
expected and measured values. 
\item ?
\end{enumerate}
In all of the above procedures, did your measurements indicate that  $\int{\cal E}dt=-\Phi$
or ${\cal E}=-\frac{d\Phi}{dt}$ as predicted by Faraday's Law?

\subsection{Observe Useful Magnetic Induction Systems}
\begin{enumerate}
\item repeat one of the above with a iron core
\item repeat one of the above with a brass core
\item transformer
\item Electric generator
\item Inductance
\end{enumerate}

\subsection{Questions}
draft questions
\begin{itemize}
\item If the solenoid had a resistance of 1 kilohm and a resistor of 2 kilohm were placed across
the solenoid, and an emf of ${\cal E}=10.0$ volts was induced in the solenoid,
what voltage might be measured across the resistor?\\
\item If no resistor is added and the angle $\theta$, between the solenoid and the magnetic field, were changed at a
rate $\omega=\frac{d\omega}{dt}$, and the maximum emf found across the solenoid is
${\cal E}=10.0$ volts, what would be the equation for the voltage at any time $t$?\\
\item Describe three common applications of magnetic induction\\
in most homes,\\
near but outside most homes in Madison,\\
in all cars.
\item ?
\end{itemize}
\newpage
%
%-----------------------------------------------------------------------------
%
\section{E7.~~Electromagnetic~induction (BC)}
\noindent OBJECTIVE: %\vspace*{.1in} \\
To study electromagnetic induction and to 
verify Lenz's law.\\ 


%\subsection{Preliminary Questions}
%\begin{enumerate}
%\item ?
%\item ?
%\item ?
%\item ?
%\end{enumerate}

\noindent APPARATUS: \vspace*{.1in} \\
\begin{mp1}
Two coils: the {\em first} a
primary, the {\em second} a many-turn secondary; 
galvanometer; rod magnet; 
brass and iron rods; electronic power supply; 
switches; small compass; (optional:  model generator/motor).

\begin{enumerate} 
\item[]{\em CAUTION:}  
If a magnet is placed or stored close above or below the compass needle, 
the needle may remagnetize to opposite polarity. \\
\end{enumerate}

\end{mp1}

\noindent INVESTIGATIONS: \vspace*{.1in} \\ 
\begin{mp2}
\begin{enumerate}
\item With the compass explore qualitatively the magnetic field near 
the bar magnet: first check that the compass 
needle points north, (see CAUTION above).  Sketch the field pattern, and 
put arrows on the field line. \vspace*{.05in}  \\
\begin{minipage}[h]{2.5in} \item 
Similarly explore the field of the primary coil after closing the 
switch of the Fig.~1 set-up. Sketch the results.
\end{minipage}

\vspace*{.05in}

\hspace*{4in} Fig.~1

\item To test which way the galvanometer deflects for a given current 
direction, connect the dry cell's (-) terminal to the left terminal of the 
galvanometer; then connect the dry cell's (+) terminal {\bf through your body} 
to the galvanometer.  Unless your skin is very dry, enough current should 
flow to give a small deflection. \\
\end{enumerate}
\end{mp2}

\noindent SUGGESTIONS: \vspace*{.1in} \\  \begin{mp1}

With coil axes aligned horizontally, place the two coils end to end.
Connect the primary as in Fig.~1, but connect the secondary to the 
galvanometer.  Use long (about 1 m) leads for both coils.  
Note the direction of the current in the primary.

\noindent Specify currents as clockwise or counterclockwise as 
viewed always from the right. Tabulate the results of the experiments 
as follows:
\begin{tabbing}
\hspace*{.2in} Action \hspace*{.8in} \=  
~~~~~Direction of current \hspace*{.8in}\=  Size of deflection\\
\>Primary \hspace{.5in} Secondary \> ~(if appropriate)\\
Closed primary \\
~~~switch\\
\end{tabbing}
\end{mp1}
\medskip
\vspace*{.3in}

\begin{center} EXPERIMENTS ON INDUCTION \end{center}
 
 \hspace*{-.35in}
\begin{mp2} 
\begin{enumerate}
\item Note the current direction in the secondary when primary 
switch is closed, and then opened.  Explain in terms of Lenz's law.
\item With primary switch closed move secondary away from primary;  then toward 
primary.  Note directions of secondary currents.
Now repeat but move the primary instead of the secondary.  Explain in 
terms of Lenz's law.
\end{enumerate}
\end{mp2} \newpage \hspace*{-.35in}
\begin{mp2}
\begin{enumerate}
\item[3.] With the coil axes aligned horizontally (and with 
switch closed), rotate the secondary coil in 90$^o $ steps about a vertical 
axis through the secondary coil.  Record the current directions in 
each step.  Explain in terms of Lenz's law.
\item[4.] With the coil axes aligned but separated by several 
centimeters, 
\begin{enumerate}
\item[a)] note deflection size as one closes and opens the primary 
circuit. 
\item[b)] Repeat with the soft iron rod inserted along 
the axes of the coils.  
\item[c)] Repeat with a brass rod instead of the iron rod.  
\item[d)] Explain the results.
\end{enumerate}
\item[5.] For the Fig.~2 set-up, 
keep S$_2$ open, but close S$_1$.  Wait several seconds, and 
then close S$_2$.  Does current flow in the galvanometer?  Explain.

\vspace{.5in}
Fig.~2

\vspace{.5in}

\item[6.] Remove the iron rod of Fig.~2 and reconnect secondary directly to 
galvanometer.
With primary circuit open, note the deflections as you move a magnet's
{\bf north} pole 
toward and then away from the {\bf right} end of the secondary; then 
toward and away from the {\bf left} end of the secondary.  Repeat the first 
observation but with the {\bf south} pole of the magnet.
\item[7.] Twist the leads to the secondary so area enclosed by leads is small and 
remains constant.  With S$_1$ open and with
all magnets removed from the vicinity of the secondary coil, place 
the secondary coil on the table with its plane horizontal.  
Keeping its plane horizontal, raise it quickly (vertically) 
through 10 or 20 cm.  Lower 
it to the table top.  Rotate it though 180$^o $ about a horizontal axis.  
Explain any deflections which you observe.
\end{enumerate}
\end{mp2}
\medskip
\begin{mp2}
\noindent {\em OPTIONAL:}
Experiment with the model generator/motor: e.g.~connect
the output of the generator to the galvanometer and 
turn the generator slowly.  Try both slip ring and commutator connections.
\end{mp2}
