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suspending thread and is repelled and stands out at an angle from
the vertical brass support. Since the greater the charge the
greater the repulsion and the greater the angle at which the pith
ball stands, this instrument indicates roughly the relative amount
of the charge.

The gold-leaf electroscope, a much more sensitive form, is de-
scribed further on (Par. 34).

26. Simultaneous Production of Equal Amounts of Both Kinds
of Electricity. In producing electricity by friction the body
rubbed acquires a certain kind of charge and the rubber acquires
the other kind; thus in rubbing a glass rod with silk the rod is
charged with vitreous or positive electricity and the silk can be
shown to have a resinous or negative charge. Furthermore, as



16 ELEMENTS OF ELECTRICITY.

may be shown in several ways, the amounts of the two kinds are
exactly equal. If two substances are rubbed together and -acquire
opposite charges and their charges be imparted successively to a
third body the third body will not be electrified. If a disc of glass
and one covered with silk, both being mounted on glass handles, be
rubbed together they will each separately attract pith balls but
when placed together will have no effect, the charge on the one
exactly counterbalancing or neutralizing that on the other.

27. Theories of Electricity. Two theories were advanced to
account for the above phenomena. The first is Symmer's Two
Fluid Theory. According to this there exist in all bodies two
electrical fluids of opposite kinds but in exact balance, thus neutral-
izing each other. When a body is excited by friction this balance
is disturbed and one of the fluids is drawn off upon the rubber
leaving the remaining fluid unbalanced and in excess. In this
country the theory most generally accepted is Franklin's Single
Fluid Theory. In brief this is to the effect that all bodies in their
natural state are charged with a certain quantity of electricity,
in each body this quantity being of definite amount. When two
bodies are rubbed together one parts with a portion of its electric-
ity which is appropriated by the other. The latter then has more
than its normal share and is positively electrified; the former has
less and is negatively electrified. It is proper to state here that
although we do not know what electricity is, we do know that it
is not a fluid yet we retain the term for convenience, and that
although we speak of bodies being positively or negatively elec-
trified we really do not know which has the greater charge and
the terms are used purely in a conventional sense, just as in
analytical geometry distances to the right of the vertical axis are
by convention considered positive and those to the left negative.
Finally, no satisfactory explanation is given why bodies should
acquire unlike charges by friction. The amount of electrification
is not proportional to the amount of mechanical energy spent in
friction, since it is immaterial whether the friction be of the ordi-
nary kind or be rolling, but it is proportional to the amount spent
in pulling apart two bodies held together by the mutual attraction
due to their opposite electrical states.



STATIC ELECTRICITY.



17



CHAPTER 4.

ELECTROSTATIC INDUCTION.

28. Electrification by Influence. In Fig. 7, A represents a
metallic ball attached to a stand by a glass stem and B a metallic
cylinder similarly mounted and carrying on its under side a series
of pairs of pith balls hanging from linen threads. So far as elec-
trical results are concerned, it is immaterial whether the ball
and cylinder be solid or hollow. They may even be of wood
covered with tjn-foil or gilded but are usually made of thin brass.




C



A A



B



Fig. 7.

If now the ball A, while at some distance from B, be given a charge,
say positive, and then be moved up towards B, the pith balls
beneath B will be observed to diverge indicating that B is charged.
Since A has not touched B and since the same effect is produced
when a sheet of glass is interposed between A and B and, finally,
since it can be shown that the charge upon A is undiminished, the
charge upon B could not have been communicated from A but
must have been induced or produced by the influence of A's charge.
This phenomenon may be called "induction" but, as will be seen
later, there is a more important and different kind of induction
and it is better to use the term "influence" If A be withdrawn,
the charge upon B disappears.

29. Distribution of the Induced Charge. If we return to the
preceding experiment and examine B while it is under the in-



18 ELEMENTS OF ELECTRICITY.

fluence of A, it will be noticed that the pairs of pith balls do not
diverge to the same extent, those at the ends standing far apart
but the divergence decreasing towards the center and the pair at
the center not diverging at all. This indicates that the charge
has accumulated at the ends of B and that the center is not charged.
Examination with an electroscope will show that the charges at
the ends of B are of different kinds, that nearest A (in the case
assumed) being negative, that farthest away being positive; in
other words, the positive charge on A has induced on B and drawn
as near to itself as possible a negative charge and repelled as far
as possible a positive charge.

In Par. 24 it is stated that bodies charged with like electricity
repel each other and those charged with unlike attract. The
above experiment seems to indicate that it is not the charged
bodies that attract or repel each other but the charges them-
selves; however, as we can not obtain a charge separate from a
material body the matter is not susceptible of absolutely convinc-
ing proof.

30. Electric Attraction and Repulsion Explained. The fore-
going affords an explanation of the phenomena of attraction and
repulsion already described. When an electrified rod is presented
to a pith ball, a like charge is induced on the far side of the ball
and an opposite charge on the near side. The like charge is
repelled, the opposite attracted and the opposite being the nearer,
the force of attraction is greater than that of repulsion and the
ball moves bodily to the rod. Upon contact with the rod
the opposite charge on the ball is neutralized by a portion of
the charge on the rod, leaving the ball with the same kind of
charge as that remaining on the rod and consequently the ball is
repelled.

31. Amount of Induced Charge. A given charge always in-
duces on surrounding objects an exactly equal opposite charge.
If a small charged sphere be placed at the center of a hollow con-
ducting sphere there will be induced upon the inner surface of the
latter an exactly equal opposite charge, and this no matter
what the size of the outer sphere or the thickness or the nature
of the intervening non-conductor. If the charged sphere be dis-
placed from the center so as to be nearer one side of the cavity
than the other, the amount of the induced charge is unaltered



STATIC ELECTRICITY. 19

but the greater portion will accumulate upon the side of the
cavity nearest the sphere. A charged body inside of a room
induces upon the ceiling, walls, floor and surrounding objects
opposite charges which in the aggregate exactly equal the central
charge and which accumulate most upon those objects nearest
to it. Finally, if the charged body be at a distance from others,
as for example in an open field, the induced charge will still be the
same but will be spread over the surface of the ground, the greater
portion being immediately beneath the body. If while in this
position a conducting body be brought up close to it, practically
the entire induced charge will be found upon the second body and
the portion upon the earth becomes so small that it may be
neglected. In ordinary laboratory experiments where the charged
body is a foot or more from the table beneath and is supported
by an insulated stem and the conductor upon which the charge is
induced is brought up to a distance of an inch or so from the first,
the induced charge upon the table and more distant objects
becomes less and less and gathers more and more upon the con-
ductor. Under such conditions we may say that the amount of
the induced charge upon the conductor depends upon

(a) The amount of the primary or inducing charge;

(b) The distance between the primary and the induced charge;

(c) The nature of the medium between them.

The greater the primary charge, the greater its influence and the
greater the induced charge.

The nearer the primary charge to the conductor, the greater
the induced charge.

With a constant primary charge at a constant distance from the
conductor, the amount of the induced charge is found to vary with
the nature of the separating medium, that is, whether it be air or
oil or glass or sulphur or mica or other non-conductor and this
variation is not in proportion to the value of the substance as a
non-conductor but to an inherent property of the substance
termed by Faraday its dielectric capacity (see Par. 90).

The maximum charge that could ever be induced is one at the
far end of the conductor equal and similar to the primary charge
and one at the near end equal and opposite. As the distance
between the primary and the opposite induced charge diminishes
a point is reached where the attraction between them becomes



20



ELEMENTS OF ELECTRICITY.



great enough to break down the resistance of the remaining
thickness of the medium intervening, a spark leaps across, the
primary charge and the opposite induced charge neutralize each
other, the original charged body is found to be discharged and
the conductor is left charged with the similar charge which at
first was repelled to its far end.

32. Separation of the Induced Charges. If we repeat the pre-
ceding experiment with the charged ball A and a divided con-




c



B



w




ductor consisting of two parts B and C, Fig. 8, which may be
placed in close contact, the induced positive charge will be repelled
Into the far end C and the negative charge drawn into the near
end B. While under the influence of A, C may be removed first
and then B and each will be found to be charged, C positively and
B negatively. If the two parts while distant from A be again
, joined together their electrifica-

" tion vanishes. This is an addi-




c



B



~"\ tional proof of the fact stated

/ in Par. 26 of the simultaneous

production of equal amounts of
both kinds of electricity.

33. Free and Bound Charges.

Let us again consider the case
of the charged insulated ball and
the insulated conductor as shown
in Fig. 9. The positive charge on
A has induced and attracted to the near end of B a negative
charge which is held securely by their mutual attraction. The
hand may be placed on B, a wire may be attached to the near



Fig. 9.



STATIC ELECTRICITY. 21

end of B f still the negative charge refuses to budge and the only
way by which it can be made to shift its position is by connect-
ing it to some conductor which will allow it to approach A nearer
than it is now. Such a charge, that is an induced charge held by
a primary charge of the opposite kind, is said to be "bound."
On the other hand, the positive charge on the far end of B is
being repelled by A and will take advantage of any path what-
soever which will enable it to withdraw more remote from A.
Thus if the hand be placed upon the near end or upon any other
point of B the positive cliarge immediately escapes through the
body and finally to the earth, even though in doing so it must
in a part of its pathway draw nearer to A. Such a charge, in
contradistinction to the bound charge, is said to be "free" and
this name is also applied to any charge upon an insulated con-
ductor not under the influence of some other charge. Since the
free charge always escapes when the conductor is touched and the
bound charge remains, the following rule is given : // while under
the influence of a charged body a conductor be touched, it acquires a
charge of the opposite sign.

We are now in a position to understand the operation of
two pieces of apparatus, the gold-leaf electroscope and the
electrophorus.

34. The Gold-Leaf Electroscope. This is a very sensitive piece
of apparatus for detecting the presence of electric charges and
determining their character. The simplest form consists of a
glass jar (Fig. 10) closed by a stopper of insulating material
through which passes a brass rod which terminates above in a
metal knob or disc and below is bent like the letter L. Fastened to
the horizontal arm of the L so as to hang face to face in contact
and vertically are two small ribbon-like strips of gold-leaf. This
is used because on account of its extreme thinness it is lighter than
any other material of equal strength and adds the advantage of
being an excellent conductor. The glass jar serves as an insulating
support and protects the leaves from currents of air which would
cause them to flutter. When a charged body, such as an electri-
fied rod of glass or of sealing wax, even though the charge be very
small, is brought within a foot or so of the apparatus the hanging
leaves will diverge. The explanation is that the charged body
induces and attracts an unlike charge into the knob of the appara-
tus and repels a charge of similar kind to its own as far as possible,



22



ELEMENTS OF ELECTRICITY.



that is, into the gold leaves; these having like charges repel each
other and stand apart.

To determine the nature of a charge, the electroscope is given a
preliminary charge of a known kind. This causes the leaves to




Fig. 10.



diverge. If now it be approached by a charge of the same kind
the leaves will diverge more while if the charge be of opposite
kind they will droop together.

By taking advantage of the principle given in the preceding
paragraph we may with a single charged body impart to the
electroscope a charge of either kind desired. Thus with a posi-
tively charged glass rod we may touch the knob and impart a
slight positive charge (we really neutralize the induced negative
charge in the knob and leave the induced positive charge). To
charge it negatively we hold the glass rod near the knob (Fig. 10).
This induces a bound negative charge and a free positive charge.
If now the knob be touched by the remaining hand the free charge
will be removed as will be indicated by the leaves instantly falling
together. Now withdraw the hand and finally remove the rod.
The bound negative charge, which had been attracted into the
knob, will surge back and distribute itself as will be shown by the
leaves again diverging.



STATIC ELECTRICITY.



23




35. The Electrophorus. Volta's invention, the electrophorus,
Fig. 11, an instrument for producing static charges by influence,
consists of two parts. The first,
analogous to the charged rod used in
the experiments described in the pre-
ceding paragraph, is a flat cake of
some resinoid body, resin, sealing
wax, sulphur, vulcanized rubber or
celluloid, mounted in a shallow
metal dish. The second^is a circu-
lar disc of metal, or of wood covered
with tin-foil, at the back of which is a
glass handle. To use the instrument,
the cake dry and free from dust is
rubbed with a warm, dry, woolen

cloth or piece of fur. It thus acquires a negative charge. The
metal disc is then placed upon the cake. It is in mathematical
contact with the cake in only a few points and the cake being a
non-conductor only the minute portions of the charge at these
points of contact flow into the disc. Therefore the disc is a con-
ductor separated from a charged body, the cake, by a layer of air
as thin as a sheet of paper and consequently a bound positive
charge is induced upon its lower face and a free negative charge
upon its upper face. While in this condition it is touched by the
finger, the free charge escapes and, in accordance with the rule in
Par. 33, it is left with a positive charge. It may then be lifted by
the glass handle and its charge being no longer bound can be used
to give a spark, to charge other bodies, etc. As practically none of
the primary charge on the cake is removed, this process could be
repeated an indefinite number of times without the necessity of
recharging the cake but, as a matter of fact, the primary charge
gradually weakens due to leakage into the air.

In the production of electricity, energy must always be expended.
It requires more force to pull the disc away from the charged cake
than it does from the cake before it is charged; the extra energy
thus expended accounts for the production of the charge.

Machines have been invented by which this operation of bring-
ing up the conductor, touching it and then withdrawing it is per-
formed automatically and the movement of these machines, being
one of rotation, the production of the charge is almost continuous.



24 ELEMENTS OF ELECTRICITY.



CHAPTER 5.
DISTRIBUTION OF CHARGE.

36. Charge on a Non-Conductor. An electric charge imparted
to a body is differently distributed according to whether the body
is a conductor or a non-conductor. In the case of a non-conductor
the charge clings to the spot where it was generated or placed. If
a stick of sealing wax be rubbed, only the part which has been
rubbed will be found to be charged. If a cake of non-conducting
material be touched by a charged body, only the spots actually
touched will be charged. If such a cake be charged over its entire
surface and then be touched by the finger or by a conductor, only
the spots actually touched will be discharged. Lichtenberg
devised a means by which the above may be shown to the eye. A
charged body is moved like a pencil over a dry sheet of glass or of
resin and a pattern is traced. Finely powdered red lead and
sulphur mixed together are then sifted over this pattern through
a piece of muslin. In the mixing and sifting the red lead becomes
positively electrified, the sulphur negatively, and if the original
charge be positive, the sulphur will be attracted, the red lead
repelled and there will be produced a yellow pattern on a red
back ground. In performing this experiment it will be noticed
that the sulphur does not follow absolutely the mathematical
lines originally traced but spreads slightly in mossy or frost-like
patterns. Charges while not flowing over a non-conductor still
have a tendency to creep or spread and the fern-like forms are due
to minute particles of dust which lead the charge now in one
direction, now in another.

37. Charge on a Conductor. On the other hand, a charge
imparted to any point of a conductor spreads immediately over
the entire body and if a charged conductor be touched at any point
so as to afford a path to the earth it is immediately discharged.
It is possible with the apparatus described in the next paragraph
to remove a portion of the charge. As soon as this portion is
removed the remaining charge redistributes itself.



STATIC ELECTRICITY.



25




38. The Charge Confined to the Surface. With size, shape and
other conditions constant it is found that the same charge may be
imparted to a conductor whether it be solid

or hollow or even made of non-conducting
material covered with tin-foil or gilded. The
inevitable conclusion is that the charge
resides upon the surface of a conductor. This
is shown directly by the following experi-
ments. A hollow metallic sphere (Fig. 12)
with an opening in its top and mounted upon
a glass support is given a charge. In order to
take a sample portion of a charge for in-
vestigation, Coulomb devised a piece of ap-
paratus which he called a proof plane. This
is a little circular disc of metal or gilded paper
fastened to the end of a small glass rod. If the disc be touched to
a charged body it receives a portion of the charge and may then
be removed, and the charge tested by an electroscope or otherwise.
If the charged sphere be touched by a proof plane it will part with
a portion of its charge. If, however, the proof plane be inserted
through the opening in the sphere and the inside of the sphere be
touched, the plane will show no sign of any charge.

The above fact may be even more conclusively shown as follows :
A small metal ball suspended by a silk thread is brought into con-
tact with the outside of the charged hollow sphere. While touch-
ing the sphere it is practically a portion of the latter's outer sur-
face and it receives a charge. The charged ball is then lowered
through the opening until it touches the inside of the sphere.
At that instant when it forms a part of the latter's inner sur-
face it is discharged, the charge passing through to the outside of
the sphere.

Faraday showed the same thing with a cylinder of wire gauze
instead of the sphere.

39. Blot's Experiment. -Another demonstration of the surface
distribution of the charge is given by Biot's experiment. In Fig.
13, A is an insulated metallic sphere and B and C are glass-handled
metallic hemispheres slightly larger than the sphere. If the sphere
be charged and then the hemispheres placed so as to completely
cover it but not to touch it the charge will still remain on the sphere.
If the covers be allowed to touch the sphere the charge will im-



26



ELEMENTS OF ELECTRICITY.



mediately pass to the hemispheres which when separated will be
found to be charged and the sphere discharged. The reason for
this is given later (Par. 68).



c



B




Fig. 13.

As an exception to the foregoing general statement there is one
set of conditions under which it is possible to have a charge on the
interior of a conductor. If through the opening of the sphere
shown in Fig. 12 there be inserted a charged insulated body, there
will be induced upon the inside of the surrounding sphere a charge
of opposite kind, the charge of like kind being repelled to the
exterior.

Finally, it must be remembered that we are now discussing
static charges, for, as will be shown later, current electricity
penetrates throughout the conductor.

40. Distribution of Charge. Although, as was stated in Par.
37 above, a charge imparted to a conductor spreads over it im-
mediately, the distribution is not uniform but more of the charge



a



b c

Fig. 14.

will be found about the edges and angles than upon the flatter
surfaces. In fact, there is only one body, the sphere, upon which
the distribution is uniform and this is so only when the sphere is
so remote from other charged bodies that the effects of induction



STATIC ELECTRICITY. 27

are not felt. This uniform distribution may be represented
graphically as in (a) in Fig. 14 by drawing about the circle repre-
senting the sphere a concentric dotted circle as if the charge were
a material of the thickness represented by the distance between
the full and the dotted circles.

On a metallic disc (b) the charge is heaped up around the edges
but uniformly distributed over the flat surfaces. Advantage is
taken of this in a piece of apparatus, the attracted disc electrom-
eter (Par. 101).

If the conductor be a cylinder with rounded ends (c), such as
is used with many electrical machines, the amount of charge at
the ends is much greater than upon the cylindrical portion.

41. Surface Density. This material conception of the charge
is not confined to graphic representation but in o*ur calculations
we may and do treat it as if it were a substance the component
particles of which repel each other and combine in a resultant
action upon other charges. Thus we speak of it as spread with a
certain density over the surface of a conductor or as being denser
at certain points than at others. This surface density is meas-
ured by the amount of electrification or number of units of elec-
tricity per unit area. What these units are is explained later (Par.
56). An isolated sphere is the only body over which the dis-
tribution is uniform and the surface density is determined by
dividing the total charge by the area of the sphere.

On neither conductors nor on non-conductors may a charge be
accumulated indefinitely, but when in air the surface density at
any point reaches about 20 units per square centimeter a discharge
will occur either along the surface of the body or through the body
or through the surrounding medium.

42. Effect of Points. Coulomb found that in an ellipsoid of
revolution the surface density at the extremities of the axes were
to each other as the lengths of the respective axes. In a spindle-
shaped ellipsoid where the axis of revolution is much longer than
the minor axis the density at the pointed end is very much greater
than that on the equatorial surface, and this disproportion in-



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