Physics for university students (Volume 2) online

vision must be made for drawing off the repelled charge.

It is quite possible, how-
ever, to provide for the re-
moval of the attracted charge,
so that the conductor under
influence shall remain charged
with electricity of the same
sign as the influencing charge.
Imagine the conductor B pro- s~ ^.
vided with a row of sharp) j_ j
points at the end a (Fig. 58), V )

and let a circular glass plate Fig 58

be revolved with its edge be-
tween A and B. The attracted charge will then acquire
so great a density on the points that they will discharge it
on the revolving plate. If another row of points e, con-
nected with the earth, be placed opposite the same side of
the glass plate, but out of the inductive action of A, then
as the plate revolves it will give up to c the negative
charge acquired at a, and c will convey it to the earth. In
this way B is left with a -f charge. Work is done in turn-
ing the glass plate against the attraction of the unlike
charges on it and A.

127. Attraction due to Induction. The simple facts
of induction furnish an explanation of the attraction be-
tween electrified and unelectrified bodies. The induced
charge of opposite sign always accumulates on the part




174 ELECTRICITY AND MAGNETISM.

of the conductor nearest the inducing charge, while the re-
pelled charge retires to the most distant parts of the conduc-
tor, or goes to the earth if a conducting path is furnished.

If an excited glass rod O (Fig. 59) be
presented to an uncharged pith-ball sus-
pended by silk, negative electricity will be
induced on the pith-ball at a and positive
at b. Since the former is nearer than
Fig 59 the latter, the attraction will prevail over
the repulsion, and the pith-ball will on the
whole be attracted. If the pith-ball be touched while
under induction, the repelled + charge will go to earth
and the attraction will be increased.

( If the pith-ball be slightly charged positively, then the
resultant action on it will be the algebraic sum of the
repulsion due to this charge, and the attraction due to
induction. Repulsion Avill generally be first observed as
the pith-ball is brought near (7, but at smaller distances the
inductive attraction will prevail. Repulsion is therefore a
better test of an independent charge than attraction. ^

128. Relation between the Induced and the Inducing
Charges. The charge on a conductor under
induction can never exceed the inducing
charge. It must be borne in mind that the
bound electricity is held by attraction exerted
along lines of force. If all the lines from
the inducing charge proceed to the induced
charge, the two will then be equal. Gen-
erally only a portion of the lines are common
to the two charges, while the remainder go to other bodies.
If a charged ball be nearly surrounded by a hollow con-
ductor (Fig. 60), all the lines of force from the ball A will




ELECTRIFICATION BY INFLUENCE. 175

end in the induced charge on the enclosure. No sensible
portion of them will escape through the small opening.
A charge will then spread over the interior of B equal
in amount to the + charge on A.

This case furnishes an exception to the general law that
the charge is confined to the outside of a conductor; but
it is held on the inside by inductive action from J., or is a
bound charge. If B should be insulated while under
induction and A then removed without contact with B,
the charge on B would become free and would spread
over the exterior.

129. Faraday's Ice-pail Experiment. Faraday em-
ployed a pewter ice-pail as a convenient hollow conductor
to test the relative values of
the induced and inducing
charges. A is a section of a
well-insulated pail (Fig. 61).
The outside is connected with
a gold-leaf electroscope E.
A charged ball C is let down
into the pail by means of a
silk thread. As soon as it
enters the pail the gold leaves
begin to diverge, and the di-
vergence increases till the ball
reaches a certain depth. Be- Fig. ei.

yond this point the divergence

remains constant. Evidently the divergence increases up
to the point where all the lines of influence from the ball
run to the negative charge on the inside of the pail. With
the ball still lower, the distribution of the charge, both
on the inside and the outside of the pail, may be changed,
but the quantity remains the same.




176 ELECTRICITY AND MAGNETISM.

If now the ball be allowed to touch the pail, not the
slightest change in the divergence of the gold leaves can
be detected. The meaning is that the free positive charge
on the outside of the pail, when the ball is acting induc-
tively on it, is exactly the same as the charge communi-
cated by the ball on making contact. The inducing and
the induced charges are therefore, equal.

The experiment was varied by touching the pail while
under influence from the ball. The gold leaves collapsed.
On withdrawing the ball they again diverged to the same
extent as before, but with a negative charge. If then the
charged ball were replaced and made to touch the pail, all
signs of electrification disappeared, or the induced nega-
tive charge was exactly equal to the positive conveyed by
the ball.

Faraday extended these experiments by placing four
cylinders or ice-pails one within another, but all separately
insulated. The entrance of the ball caused a divergence
of the leaves of the electroscope connected with the outer
pail. No change in the divergence could be detected
when the cylinders, while remaining insulated from the
earth, were connected together one after another, showing
that the successive inductions resulted in separating equal
quantities of positive and negative electricity on each pail,
alternating with each other, the inside of each pail being
charged negatively and the outside positively.

ISO. The Electrophorus. - - The electrophorus is a
simple instrument, invented by Volta, for the purpose of
obtaining an indefinite number of small charges by in-
fluence from a single charge produced by friction. It con-
sists of a metal base or sole, a dielectric disk of resinous
material or vulcanite fitting the base, and a cover provided



ELECTRIFICATION BY INFLUENCE.



177



with an insulating handle (Fig. 62). The form shown in
the figure is so made that the handle can be screwed either
to the cover or the base. In the middle of the disk is a
hi ass stud screwed into the base and connecting the base
and cover when the latter is applied to the disk.

To use the electrophorus the dielec-
tric must first be electrified by striking
with a cat's skin. A chamois skin will
answer, but cat's fur is better. This
gives t< ) the hard rubber disk a charge,
and if it is warm and dry it will retain
its charge for some time. The cover is
then placed on the disk, touched with
the finger or to the sole, if the instru-
ment is not provided with the brass
stud to connect the two metal plates,
and is then lifted by the glass handle.
It will be found to be charged posi-,
tively to such a degree that a spark
may be obtained from it by presenting
the knuckle. The operation may be repeated an indefinite
number of times without removing any appreciable part of
the original charge from the vulcanite, since the cover
touches it at a few points only.

The operation of the instrument is easily explained by
the principle of influence. When the cover is placed
on the excited disk, it is realfyo- insulated from it and is
powerfully acted on inductively. A positive charge accu-
mulates on its lower surface and a free negative one on
the top. The latter is removed from the cover when
touched by the finger or to the base. When the cover is
lifted by the glass handle the positive charge on it is sepa-
rated from the negative on the disk and becomes free. No




Fig. 62.



178



ELECTRICITY AND MAGNETISM.



part of the original charge has been removed ; that re-
mains on the vulcanite disk to serve for the repetition
of the operation. It is slowly dissipated if the air is damp
or if the vulcanite is not dry. 1

131. Energy of the Successive Charges. Since the
successive charges on the cover in the normal use of the

electrophorus are not derived from
the disk, it is important to explain
the source of the energy repre-
sented by them ; for electrification

is a form of energy and cannot be

produced without the expenditure



* +



Fig. 63.




Fig. 64.



of energy in some other form.

When the cover is on the disk
and the charge has been removed,
it is held down to the disk by the
lines of force running from the
positive on it to the negative on
the disk. A few lines also run
from the base to the disk, as shown
in Fig. 63. Now to lift the cover without discharging it,

1 It is possible to obtain six successive sparks from the electrophorus by
one application of the cover. For this purpose the base must be placed on an
insulating stand and the cover must not come into electric contact with it. The
several operations are as follows :

(1) Beat with cat's skin and remove the repelled charge from the base.

(2) Apply the cover and remove from it the free charge.

(3) The induction on the cover diminishes the influence of the charge of
the -disk on the base and releases part of the + charge. In other words, while
the chai'ge on the vulcanite is engaged in holding the + charge on the cover, it
lets go some of the positive on the base, which may be removed.

(4) The last operation allows greater induction on the cover. Bring cover
and base into contact and a spark will pass.

(5) Lift the cover. The minus charge on the disk again attracts positive oil
the base and releases negative, which may be removed.

(6) Discharge the positive on the cover.



ELECTRIFICATION BY INFLUENCE.



179



these lines of force must be stretched and broken. As
the cover is withdrawn fewer lines run from it to the disk
and more come from the base, as illustrated in Fig. 64.
Hence to lift the cover work must be done against the
force represented by the tension of these stretched lines,
in addition to the work done against gravity. This extra
work is equal to the energy of the charge.



Lord Kelvin's 'Water-dropping Accumulator.
-This interesting device illustrates the accumulation of
electric charges by influence, and serves as an introduction
to the continuous electrophorus, or influence machine,
u bunt to be described.

A and B are two insulated hol-
low conductors electrically insu-
lated and called inductors (Fig.
: A' and B' are two others
called receivers, all shown in sec- A
tion. (7 and Dare pipes from which
water issues in drops at the middle
of A and B. These conductors are
initially charged with very small
positive and negative charges.

The operation is as follows : As
drops issue from the two nozzles
they are influenced inductively,
since they are not completely sur-
rounded by the hollow inductors.
those in A have a charge and those in B a + one.
The two lower cylinders or receivers contain funnels
which receive the drops and their charges, thus increasing
the electrification of the two sets of conductors. The
effect is cumulative, and the electric density increases till




Fig. 65,.



When the drops fall.



180



ELECTRICITY AND MAGNETISM.



sparks pass between parts of the apparatus, or the water-
drops are scattered about over the edges of the receivers.
It is essential that the two streams shall be discontinuous
or be broken into drops.

The energy of the charges is derived from the potential
energy of the falling water. The drops are attracted up-
wards and fall more gently than they would if free. Their
loss in potential energy in falling from inductors to re-
ceivers is therefore less than that corresponding to the
difference of levels, and this difference in energy is the
energy of the charges which they convey.

133. The Holtz Influence Machine (Th., 65 ; B., 584).
- It was long ago. seen that if the principle of the elec-




Fig. 66.



trophorus could be made to act continuously by mechanical
means, an influence machine could be constructed which
would be superior to the old method of producing electrifi-
cation by friction. This has been accomplished by several



ELECTRIFICATION BY INFLUENCE.



181



inventors, and frictional machines have in consequence
gone out of use.

The first successful influence machine was the one made
by Holtz in 1865. Inasmuch as it has been superseded by
others having the advantage of being self-exciting, a brief
description must suffice.

A thin vertical glass plate revolves very near another of
somewhat larger diameter and fixed (Fig. 66). The fixed
plate lias two openings or windows cut through at the ends
of a horizontal diameter. Extending from these openings
on the back of the plate are two long sectors of paper, pro-
vided at the windows with tongues or notched edges point-
ing toward the back of the revolving plate. These sectors
constitute the field plates or armatures. They extend about
60, and opposite their extreme ends in front are two metal
combs connected by a
diagonal neutralizing
rod, running along a
diameter. The two
other combs in front of
the rotating plate and
just opposite the win- A|
dows are collecting
combs connected with
the two discharge balls.

To explain the action
it is best to adopt the
diagrammatic method
of Bertin, in which the
two plates are shown as two concentric cylinders (Fig.
67). A and B are the field plates, g and h the neutraliz-
ing brushes, and A' and B' the collecting combs joined to
the balls .y and -P, between which the discharges take place.



\ \




Fig. 67.



182 ELECTRICITY AND MAGNETISM.,

To start the machine N and P are brought together,
and one paper sector, as J., is feebly excited positively
by contact with the charged cover of the electrophorus,
or by induction from excited vulcanite. As the glass disk
is revolved the induction between e and 17 causes the latter
to discharge negative on the front of the plate, while
positive is repelled to the other comb h and is there
discharged on the plate. When the negative comes
round to the window at B, it acts inductively 011 the paper
armature B and on the comb B'. Positive is discharged on
the plate from both of these, leaving B negatively excited.
At the same time the + discharge on the plate at h is carried
around to the window at A, where it attracts from both
A and A', leaving both +. The continuation of this action
results in the intense excitation of the two armatures or
field plates. It will be observed that the arrangement is
such as to carry away in each case the attracted charge, or
the parts are charged by influence in such a way that the
inducing and the induced charges have the same sign.

Turning now to the combs A' and B', the balls N and P
may be separated, and the induction from A and B and from
e and f keeps the upper half of the revolving plate, front
and back, charged with and the lower half with +
electricity. The charges on the front are carried off by the
combs A' and B' and unite by means of a spark between N
and P. Small Leyden jars (152) are connected with one
or both of the discharge rods for the purpose of collecting
a greater quantity for each discharge.

134. The Toepler (Voss) Machine (Th., 59; B., 588).
- The only advantage possessed by this form of machine
is that it is self-exciting and will work in a damp atmos-
phere when the Holtz will not. There are no windows in



ELECTRIFICATION BY INFLUENCE.



183



the fixed plate, and underneath the paper armature c and
L J are three disks of tin foil connected by a narrow strip
of the same material, as shown in Fig. 68. To the front of
the revolving plate are pasted at equal distances six or
eight small tin-foil disks with a low metal button in the
centre of each. The tin-foil disks on the fixed plate are
electrically connected to bent metal rods, as shown at a




Fig.



and a f These carry in front tinsel or fine wire brushes,
which, touch the metal buttons on the revolving plate as
they pass under them. The diagonal neutralizing rod has
tinsel brushes in addition to the combs. The small disks
on the front plate are rotating carriers, and each is charged
inductively by being placed in momentary connection with
one under opposite electrical influence. At the same time
the points on the neutralizing rod discharge on the revolv-
ing plate, as in the Holtz machine.



184



ELECTRICITY AND MAGNETISM.



The action may be explained by the aid of the diagram
(Fig. 69). The neutralizing brushes are set so as to con-
nect the carriers, as b and e, just before they pass beyond
the influence of the armatures A and B. They thus acquire

by influence and +
charges respectively.
Passing on to the po-
sitions c and /", they
are brought into mo-
mentary contact with
B the armatures by a
and a', and deliver up
to them their small
charges. This action
is repeated by each
pair of carriers, how-
ever small may be the
initial excitation of

In this way A becomes more highly -f and
When the carriers are highly charged




69.



A and B.

B more highly .
they do not give up their entire charges to the armatures,
and the collecting combs A / and B' receive the residue in
addition to the charges carried on the glass. There is
usually enough excitation by friction or by contact of dis-
similar substances to start the machine.



The Wimshurst Machine (Th., 61; B., 589).-

Wimshurst's influence machine is the simplest of all in
construction, and is very effective. Both glass plates ro-
tate, but in opposite directions. They are provided with a
number of narrow tin-foil sectors arranged radially on the
outer sides (Fig. 70). These strips act both as carriers
and as inductors. Across the front is fixed a diagonal



ELECTRIFICATION BY INFLUENCE. 185

conductor, armed at both ends with tinsel brushes. Across
the back is another rod at right angles to the one in front.
Its brushes touch the metal sectors on the back plate. Col-
lecting and discharging apparatus is added to utilize the
charges produced. These must be well insulated from




Fig. 70.

each other on the two sides of the machine. Leyden jars
may be used as in the other machines.

The action will be understood from the diagram (Fig.
71), in which again the two plates are represented as sec-
tions of concentric cylinders, after Bertin and Thompson.
The inner cylinder represents the front plate, and the
outer one the other. Suppose a back sector to receive a
slight charge. As a front sector a passes the outer charged
one, it is acted on inductively and an electric displacement



186 ELECTRICITY AND MAGNETISM.

takes place along the conductor, leaving a slightly charged
negatively, while b receives a corresponding + charge.
These small charges will be carried forward opposite c and
d. Here c and d are touched by the brushes at the back,
and at the same instant are under the influence of the
and + charges on a and b respectively. They will, there-
fore, receive + and charges, and will convey them in the
opposite direction to the motion of the front sectors. All
the sectors will thus become highly charged by the cumu-
lative effect of reciprocal
influence, the front sec-
tors on the upper half
carrying charges from
left to right, and the
back sectors carrying -f

^ charges from right to
left. On the lower half
of the plates a similar
but inverse set of opera-
tions occurs. Each metal
sector is alternately un-
der influence and acting
as an inductor.. By this

double action charges are continually conveyed by both
plates to the right and + ones to the left. The collecting
combs draw off these charges and convey them to the dis-
charging balls.

In all influence machines the plates are turned in oppo-
sition to the attractions between unlike electrifications.
Hence, more work is done in turning the plates when the
machine is in operation than when it is not excited.

The stress between the fixed and movable parts, or
between parts moving in opposite directions, is an opposing




ELECTRIFICATION BY INFLUENCE. 187

stress, or tends to turn the plates in the direction opposite
to their proper motion as a generator. All these machines
are therefore reversible, or may be rotated backwards as
motors, by communicating to their armatures a continuous
supply of electricity.



188 ELECTRICITY AND MAGNETISM.



CHAPTER XIII.

ELECTRICAL POTENTIAL.

136. Definition of Potential. The term Potential was
introduced by George Green, of England, in 1828, but his
theorems connected with it remained unknown till most
of them had been rediscovered by Lord Kelvin, Clausius,
aftd others. This function plays a highly important role
in the study of electrical phenomena. It is intimately
connected with the law of Conservation of Energy, and
has had an important bearing on the progress of electrical
theory and practice.

Consider two similar electrical charges left to themselves.
The mutual repulsion between them will cause them to
move apart till they are beyond each other's influence.
The mutual potential energy of such a system in any given
position is the work done by their mutual repulsion in
separating them to an infinite distance, or in conveying one
of the charges to the boundary of the field produced by
the other.

The potential at any point, due to a given positive
charge, is the mutual potential energy between this charge
and unit quantity of positive electricity placed at the point.
It is the same as the work which must be done on a posi-
tive unit of electricity in bringing it up to the point from
an infinite distance, or from the boundary of the field of
force due to the given charge. If the potential is assumed



ELECTRICAL POTENTIAL. 189

to be zero at some place chosen as a standard of reference,
then any point will have a positive potential if work must
be done in bringing a positive charge from the zero point
to it, and negative if work is required to convey a positive
charge from it to the zero point. For convenience the
potential of the earth is usually taken to be the arbitrary
zero. Positive electricity, left to itself, tends to flow along
lines of force toward points where the potential is lower;
negative electricity travels toward higher potentials.

137. Difference of Potential. Consider two points,
A and B, and let the potentials at these points be repre-
sented by Fi and V* respectively. Then since work equal
to Vi is required to convey a unit of + electricity from an
infinite distance to the point J., and a quantity V* from an
infinite distance to the point B, it is obvious that the work
done by the electrical forces in displacing a positive unit of
electricity from the one point to the other is V\ V 2 . The
work is independent of the path followed in going from A
to B ; otherwise it would be possible, by making a quantity
of electricity circulate between A and B by suitable paths,
to produce an infinite quantity of work without an equiva-
lent expenditure.

138. Equipotential Surfaces. An equipotential sur-
face is the analogue of a level surface. It is a surface per-
pendicular at every point to the direction of the force ; or,
in other words, all the lines of force which it encounters are
normal to it. There is then no component of force along
an equipotential surface, and no work is spent in displacing
any quantity of electricity on such a surface. The poten-
tial at all points of an equipotential surface is therefore the
same.



,&*,'?

190






^






Consider two such surfaces Si and $,, whose potentials
are FJ and F> . The work which must be done in displac-
ing the unit quantity from the one surface to the other is
then the difference of the two potentials, or Fj K>. It is
independent of the path travelled and of the position of
the point of departure and the point of arrival on the
two surfaces. If a quantity q units is conveyed from
one surface to the other, the work required is q times
as great as for one unit, or q ( FJ F) . The numerical
measure of the electrical work is therefore a product of two
factors, one of them a potential difference and the other a
quantity of electricity. If the potentials of the two sur-
faces differ by unity, then one erg of work must be spent
in conveying the unit quantity from one surface to the
other. x



yj, 139. Expression for Force in Terms of Potential.
Let there be two equipotential surfaces, S and >S V , very
near together (Fig. 72), and let their po-
tentials be V and V. Let F be the con-
stant force along a normal between P
and P' equivalent to the variable one be-