\subsection*{EC-6d~~Induction - Faraday Discovery}

\noindent INTRODUCTION: \latex{\vspace*{.05in}}   \\
\pind{Michael Faraday (1791-1907) 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. 
}
\pind{
~~~~~~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.}\medskip


\noindent OBJECTIVES:  \latex{\medskip}   \\ \pind{
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}}
\vspace*{-.05in}
\caption{Faraday's experiment}
\end{figure}

\pind{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}}
\vspace*{-.05in}
\caption{The square wave}
\end{figure}



\noindent EQUIPMENT: \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[$\Rightarrow$]\vspace*{-.08in} PC and interface, with the power amplifier plugged in port A. 
\item[$\Rightarrow$]\vspace*{-.08in} Two voltage sensors are plugged in the interface. The voltage sensor
plugged in the 
B port measures the voltage across the external resistor; 
the voltage sensor
plugged in the C port measures the voltage across the coil.
\item[$\Rightarrow$]\vspace*{-.08in} Computer Controlled Power Amplifier.  
\item[$\Rightarrow$]\vspace*{-.08in} 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[$\Rightarrow$]\vspace*{-.08in}
A plug board and a $100~\Omega$ resistor. }
\end{enumerate}


\noindent  PROCEDURE I: (15 min) \latex{\vspace*{-.03in}}  \begin{enumerate}
\epind{
\item[1.]\vspace*{-.05in} \vspace*{-.05in} Click on the Launch EC-6B icon below (web version) to initiate
the PASCO software window.
\item[2.]\vspace*{-.05in} 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[3.]\vspace*{-.05in} Check that the amplitude is $\sim$ 4 Volts, and the frequency is 
$\sim$ 10 Hz.
CLK on the ON button of the Signal Generator, then DCLK on RECORD.
DCLK on STOP after a second.}
\end{enumerate}
\vspace*{-.15in}


\begin{figure}[h] \centering 
\latex{\includegraphics[height=7.0cm]{figs/l104/fec6d-3.eps}}
\html{\includegraphics[height=7.0cm]{figs/l104/fec6d-3.eps}}
\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}}
\vspace*{-.05in}
\caption{The physical setup}
\end{figure}

\begin{enumerate}
\epind{\item[4.]\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 the current flowing in the coil. \\
-the other
curve (curve B) shows the induced voltage across the secondary coil
\item[5.]\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}]
}
\end{enumerate}
\indent QUESTIONS  \latex{\vspace*{-.03in}}  
\begin{enumerate}
\epind{
\item[Q1]\vspace*{-.05in} 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]\vspace*{-.05in} 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]\vspace*{-.05in} Are the peaks of voltage across the secondary coil, that correspond
to current on vs. current off 
of the same polarity? Explain.
}
\end{enumerate}

\noindent PROCEDURE II: (15 min) \latex{\vspace*{-.03in}}  
\begin{enumerate}
\epind{
\item[1.] 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[2.] CLK on the ON button of the Signal Generator, then DCLK on RECORD, 
DCLK on STOP after a second.
\item[3.] 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[4.] 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}]
}
\end{enumerate}

\indent QUESTIONS  \latex{\vspace*{-.03in}}  
\begin{enumerate} \epind{
\item[Q1]\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]\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]\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}

