\section{E-1:  Electrostatics}\label{e01_estatics}

\begin{center}
PART I. THE ELECTROSCOPE
\end{center}

\noindent
OBJECTIVE:  To use an electroscope to study electrostatic phenomena. \medskip


\noindent APPARATUS:
\begin{enumerate}
\item  \latex{\vspace*{-.07in}} 
A wooden box containing: 
aluminum-leaf electroscope, insulated hollow sphere
proofball, hard rubber rod, rabbit fur, lucite rod, silk cloth.
\end{enumerate}

\noindent
INTRODUCTION: 
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}} In this lab you will use a deceptively simple device, an
electroscope, to study the nature of charge.  The electroscope's primary working
parts are two connected conducting foil leaves.  Charge appears in two forms,
positive and negative, and like charges repel.  At this point the only
meaningful distinction
between a conductor and an insulator is that a conductor allows charge to flow
(in analogy to water in a pipe) whereas insulators do not.  Thus as charge is
placed on  (or near) the conducting electroscope knob at top,
the like charge in the electroscope assembly  
will redistribute so as to move as far away from charge on the rod and
electroscope 
as physically possible.
Since the hanging foil leaves of the electroscope are extremely lightweight
the repulsive force between the like charges on each leaf is sufficient to force the leaves
apart;  the greater the charge the greater the angular displacement.
In the schematic below we demonstrate the physical response.
\begin{figure}[h] \centering 
\latex{\includegraphics[width=5.0in]{figs/e1-01.eps}}
\html{\includegraphics[width=6.0in]{figs/e1-01.eps}}
\vspace*{-.07in}
\caption {{\em Qualitative} schematic of electroscope response.}
\end{figure}
\vspace*{-.1in}
\begin{description} 
\item[{\em Preliminary Question:}] Will the charge in the electroscope assembly redistribute itself
if a charged object is brought close to (but does not touch) the conducting
knob?  If so, will the net charge on the knob be of the same or opposite
sign?  What will be the sign of the charge on the foil leaves
be?
\end{description}
\end{enumerate}


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{\em Suggestions and precautions}  
\begin{enumerate}
\item In humid air insulators may adsorb enough moisture 
that charges leak off rapidly.  If so, dry all insulators with a heat gun.
\item In very dry or cold weather the humidity is so low that 
clothing, table tops, etc.~become good insulators.  Their large
surface charges may influence nearby unshielded instruments.
If so, ask your instructor 
for help; e.g.~use grounded foil to shield against them.
Also remove any clinging loose bits of fiber (e.g.~silk or rabbit fur) that may 
disturb results.

\item The fragile leaves of the electroscope may tear if charged too heavily.
{\bf Do not disassemble electroscope} to attempt repair:  see your instructor.
\item To remove charges on the glass windows of the electroscope, 
lightly rub your hands over the windows while grounding your body.

\hspace*{3.5in}
\latex{\includegraphics[width=1.80in]{figs/e1-02.eps}}
\item  \html{\begin{tabular}{p{4.5in}c}} 
\latex{\vspace*{-1.3in}}{\latex{\rightskip=2in} Charges on the insulating handle of a proofball 
can cause serious measuring errors. Test the
handle by grasping 
the ball with one hand (while the other hand touches the electroscope
ground), and then bring parts of the
insulating handle close to the electroscope
knob.  If the leaves move, the handle 
is charged. \smallskip\par}
\html{& \includegraphics[width=1.80in]{figs/e1-02.eps} \end{tabular}}

\noindent \latex{\vspace*{-.04in}}To discharge it, hold the handle in a source of ionized air.  The charged 
insulator will attract ions of the opposite sign until it is neutral.  An 
open flame is a simple source of both positive and negative ions.  The heated air 
convects these ions upward so {\bf hold the insulator at least 10 cm above open flame 
to avoid heat damage to the insulator}.
Avoid unnecessary handling of insulators because 
handling may impair their insulating capability.  (Perspiration is a salt solution which is
a conductor.)
\item \latex{\vspace*{-.04in}}Ground the electroscope {\em case} to a grounding jack near 
the electrical outlet.  Leave it grounded throughout the experiment. 
\end{enumerate}
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\noindent
EXPERIMENTS:  
\begin{enumerate}
\item \latex{\vspace*{-.05in}}Charge a rubber rod negatively (-) by rubbing with fur, 
and transfer some of the 
charge to the electroscope leaves by touching the rod to the electroscope 
knob.  See diagram A.  Note what happens when a 
(-) charged rod approaches the knob (diagram B).  Without grounding the 
electroscope, also observe and diagram what happens 
when a lucite rod rubbed with silk approaches the knob.  
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\includegraphics[width=4.6in]{figs/e1-03.eps}
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\item \latex{\vspace*{-.04in}}{\bf Charging~by~induction}   (First discharge the electroscope 
by touching the knob and case 
simultaneously.)  To {\bf charge by induction} make the leaves diverge by 
bringing up a (-) charged rod:  keeping the rod fixed, {\bf ground the 
knob} to the case, {\bf break the ground} and then {\bf remove the rod}.  Explain with 
diagrams each step of the process.  Show by diagrams what happens when a 
(-) charge is brought near the knob; a positive (+) charge.  Explain each 
step briefly.
\item \latex{\vspace*{-.04in}}In the following give the proofball a charge of known sign by 
contact with a charged lucite or rubber rod.  {\bf Use diagrams to explain and 
record results}.

\begin{enumerate}
\item[a.] Connect the hollow conductor to electroscope knob by fine wire.  
Discharge them.  Charge proofball by touching\footnote{Avoid rubbing which
may result in charge separation of opposite sign (depending on the 
proofball metal and type of insulator: ``triboelectric series'', 
see exp \#6 of Part II).}
it to a charged 
rubber or lucite rod, then introduce the proofball into the hollow 
conductor but without contacting the conductor.  (If your proofball won't hold charge, you can try cleaning or heating the handle, or putting the lucite rod into the hollow conductor directly.)  Ground the hollow 
conductor by touching it.  Note behavior of electroscope.  Break 
the ground and remove proofball.  Test the sign of charge on the 
electroscope.
 \item[b.] Repeat part a, but now ground the hollow conductor 
by touching it {\bf only on the inside} with your finger or a short conductor.  
Explain.
\end{enumerate} 
\end{enumerate}

\begin{center}
PART II. Use of ELECTROMETER (a sensitive voltmeter) 
\end{center}

\noindent OBJECTIVE: 
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}To measure potential (voltage) differences 
(i.e.~the work/charge to move a 
small test charge between two conductors) and thus, in an indirect fashion, 
charges. 
\end{enumerate}

{\bf{\em{\noindent Preliminary Questions:}} } \\
\indent 1. Does the electroscope allow you to discern the absolute sign of a charge? \\
\indent 2. If you are given a spherical conductor where does the excess charge
reside? 

\noindent
APPARATUS:
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}}PASCO electrometer \& power supply; 
two hollow conducting spheres, one open hollow sphere; two charge producing 
paddles (white \& blue), one aluminum paddle; 
proofball; insulated cup and shield:  {\bf do not carry the cup and 
shield by the 
top cover} (it may separate causing the cup to drop and become damaged); 
heat gun; alcohol lamp.
\begin{figure}[h] \centering \hspace*{.2in}
\latex{\vspace*{-.1in}}
\includegraphics[height=2.05in]{figs/e1-04.eps}
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\vspace*{-.05in}
\end{enumerate}

\newpage

\noindent INTRODUCTION:
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}}The electrometer reads the difference of  potential (in volts) between the center terminal of the
input and the grounded shield.  (Normally electrometers perform floating measurements, i.e., both the positive and negative side of the measurement is allowed to be any voltage.  For convenience our electrometer has been modified to force the negative side to be ground.)  What makes the electrometer special is that the  electrometer's input resistance is so high, $\sim10^{14}~\Omega\,$,  
that negligible current flows and hence discharging effects are negligible.  Typical
handheld voltmeters have resistances five to six orders of magnitude {\em smaller}.
(For the circuit ``layout,'' see your instructor.)  
From the several voltage ranges, choose one that gives a large but less than full
scale deflection.  Accuracy is about $\pm $~3\% of full scale. Connect the insulated cup and
shield to the electrometer as shown in the sketch.  The electrometer measures the potential
difference between the cup and grounded shield.  {\em This potential is proportional to the 
quantity of charge on the cup if the surrounding 
aluminum can furnishes a perfect shield from external charged objects}.

\end{enumerate}

\label{ElectrometerPrecaution}
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\noindent PRECAUTIONS: These are needed for reliable measurements: 
\begin{enumerate}

\item \latex{\vspace*{-.07in}}Large static charges (common in dry weather) if
applied to
electrometer input may damage the sensitive input {\bf f}ield {\bf e}ffect
{\bf t}ransistor
(``FET'').  
Minimize this possibility by {\em keeping the electrometer input grounded via 
the SHORT switch during the initial hook up and when you are done with the
experiment}.  Also use a banana plug lead to connect
the GND terminal of the electrometer to the ground jack near an
electrical outlet.  In otherwords:\\
{\bf Keep the Input switch in the ``Short before making connections'' position
whenever there is nothing connected to the input or while you are making a
connection.}  (In older models, this switch may be labled ``lock.''  It is the
left position in either case.)  After the connection is made, you put the
switch in the Input
position.  If you need to get rid of charge that may have been collected, you
can move the switch to either of the short positions, the ``momentary''
positionusually being more convenient.

\item \latex{\vspace*{-.07in}}If your clothing or hair has a net charge, the
electrometer 
reading may change if you move around.  
Hence, during a given measurement, change
position as little as possible and ground yourself (e.g.~touch
the grounded shield all the time during a measurement or connect a bare
wire from your body to ground.  Note that grounding yourself is usually a {\em 
bad} idea when working with electronics, because of the danger of 
electrocution.  Be careful not to touch any voltage sources while you are 
grounded.)

\item \latex{\vspace*{-.07in}}To remove all charge from the cup, switch the
electrometer 
momentarily to the CHECK position. (This connects the electrometer terminals
to each other so that any charge flows from/to ground).   If the meter does
not
read zero, notify your instructor.  
%For the models without outputs: The ZERO knob sets the meter to zero; {\bf
adjust to zero
%only when the input is grounded: }  i.e.~while the switch is in the ``SHORT''
%or ``LOCK'' position.

\item \latex{\vspace*{-.07in}}Always discharge paddles and cup before starting
an experiment.  To
test if an object is charged, put it into the cup and see whether the
electrometer deflects.  Conductors discharge easily by touching them to
a grounded conductor.  To discharge an insulator, you must create sufficient
ions in the surrounding air. The insulator will then attract
ions of the opposite
charge until all charge is neutralized.  An open flame is a simple source
of ionized air; the ions in the flame convect upward with the hot gas.
{\bf To avoid damage to the insulator, keep it at least 10 cm above the
flame}!


\end{enumerate}
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\noindent SUGGESTED~EXPERIMENTS: 
\begin{enumerate}
\item \latex{\vspace*{-.05in}}Rub the blue and white paddles together and determine which paddle 
has a net positive charge and which has a net negative charge.
Explain the following experiments with diagrams showing charge 
distributions, e.g.~appropriate sample diagrams for this experiment are:
\begin{figure}[h] \centering 
\vspace*{-.1in}
\includegraphics[width=5.1in]{figs/e1-05.eps}
%\caption {{\em Qualitative} schematic of electroscope response.}
\end{figure}
\vspace*{-.2in}

\item Discharge both the blue and the white paddles.  Gently rub the white and 
the blue surfaces of the paddles together.  Then:

\begin{enumerate}
\item[a)] \latex{\vspace*{-.05in}} Hold one of them near 
the bottom of the cup, but don't let it touch. 
\item[b)] \latex{\vspace*{-.03in}} Take the paddle out. 
\item[c)] \latex{\vspace*{-.03in}} Put it back in, touching the cup this time.  
\item[d)] \latex{\vspace*{-.03in}} Remove the paddle.
  
\end{enumerate}

Record the electrometer reading after each step.  Explain the results.  Was 
there any charge left on the paddle at the end?
\item {\bf Charging~by~induction:}  Momentarily ground the cup.  Charge one of 
the paddles, then:
\begin{enumerate}
\item[a)] \latex{\vspace*{-.05in}}Place paddle in cup without {\bf touching}.  
\item[b)] \latex{\vspace*{-.03in}}Again momentarily ground the cup.  
\item[c)] \latex{\vspace*{-.03in}}Remove the paddle. 
\end{enumerate} 
Note the reading after each step.  Explain what happened at each step.
\item Start with both paddles discharged. Then rub them together. 
Measure the charge on each.  Explain.  Compare the amount of charge produced 
by rubbing two paddles of the {\bf same} kind (borrow one from another group), or 
by rubbing a metal paddle on a metal paddle, etc.  (Surface ``dirt'' on one paddle 
may mean you are rubbing dissimilar paddles.  Sometimes cleaning the paddles 
with alcohol makes a big difference.)
\item Discharge the cup and the blue and white paddles.  What happens if you 
place the paddles inside the cup (without touching the cup) and, 
\begin{enumerate}
\item[a)]  \latex{\vspace*{-.03in}} you charge them by rubbing while they both are inside the cup?  
\item[b)]  \latex{\vspace*{-.03in}} Take out one paddle?  
\item[c)]  \latex{\vspace*{-.03in}} Put it back in?  
\item[d)]  \latex{\vspace*{-.03in}} Take out the other?  
\item[e)]  \latex{\vspace*{-.03in}} Take them both out? \\
            Observe electrometer reading after each step.  Explain. 
\end{enumerate}
\item QUESTION: Do only insulators acquire charge by rubbing?  Rub the aluminum 
paddle on the white (or blue) paddle.  Determine sign of effect.  Arrange 
the white, blue and aluminum paddles in a series such that the rubbed one with 
a positive charge is always higher (``triboelectric'' series).  Tribology is the
study of friction. 
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\begin{enumerate}
\item[]{\bf NOTE:}  In the remaining parts you may measure charge and still avoid spurious 
effects from charges on the insulating handles if you will touch the 
charged proofball (or paddle) to the bottom of the cup and then remove it 
from the cup before reading the electrometer.  But remember to discharge 
the cup (by momentarily grounding) before taking the next reading!  However, 
if the potential of the insulating handle is too large (e.g.~way off the 
least sensitive scale), one can still get spurious effects from leakages.
\end{enumerate}
\item Instead of frictional charging, use the DC power supply. 
The ``ground'' binding post is internally connected to earth ground. 
Adjust the voltage to $\cong $~500V. Charge the hollow sphere to 500V 
(use a copper wire to connect the sphere to the power supply). {\bf The switch must 
be in the correct position or no voltage results even though the meter may read}! 
Discharge the proofball and test that it (and handle!) have zero charge; then touch 
it to the outside of the hollow sphere and measure its charge.  Do the same 
experiment but touch inside the sphere.  What do you conclude?

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\latex{\includegraphics[height=2.50in]{figs/l104/e01-2.eps}}
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\vspace*{-.05in}
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\item Connect the power supply to an isolated solid metal sphere (shown in the next
figure).  Measure 
the relative charge density $\sigma $ at various points of the sphere (such as A, B and
C).  Charge 
density $\sigma $ is $\Delta $Q/$\Delta $A where $\Delta $Q is the charge on a 
small element $\Delta $A of the 
surface.  Since it is not practical to remove a piece of the surface, we 
place the aluminum paddle {\bf flat} against the surface and measure the charge 
on the paddle after it is removed.  This measurement gives a number only 
approximately proportional to the charge density (why?) but does give a 
good idea of the relative charge distribution.   
\begin{description} \item OPTIONAL:  Repeat step 8 but 
with paddle perpendicular to the surface instead of flat.  Can you explain 
the differences?
\end{description}
\item Discharge the second solid sphere when it is far from the charged 
sphere. Then move it  within a few centimeters of the charged sphere.  
Explore the charge distribution on both spheres with the paddle.  Observe 
carefully the polarity of charge on different parts of the second sphere.
\item Does a grounded conductor necessarily have no net charge?  
Momentarily ground the second sphere when it is near the first one, then 
move it away and see whether it is charged.  What is the polarity?  ~Explain.
\item How much deflection does one get if one applies 1000V to the 
aluminum leaf electroscope?  Compare the sensitivity to that of the 
electrometer (but do {\bf not} connect 1000V to the electrometer or to anything 
connected to the electrometer e.g.~the cup.)
\item Set the electrometer switch in the LOCK position.
\end{enumerate}
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