**K2**** Electricity**

In order to compute the energy
(ability to do work) of electric charges at rest, we consider a
body *K *with a positive unit charge, which is somewhere
at rest, isolated and far away from other bodies. We now bring a
second body *K*' with a positive unit charge into its
vicinity. This requires work as *K* repels *K*',
both bodies having a positive charge. This work equals the
product of the repelling force and the length of the path, over
which the force is overcome. We can compute it, because Coulomb's law yields the force. In general, such computations
are very involved since the force changes all along as *K *approaches
*K*'. Hence we will at first confine ourselves to
questions of a general type (of fundamental importance!) and only
show below, how to perform the calculations in individual cases.

Let the positive electric
charge be initially at an *infinite** *distance from the body (so far
that the repelling force it exercises on it, vanishes or is like
0. In practice, this distance can be assumed to be infinite.)
Take it now along any path to a point *P* of the
electrical field: This action demands the work *A*. If you
now leave the unit charge at the point *P *alone, in other
words, to the unimpeded action of the repelling body, it will be
repelled to an infinite distance and in the process it* **performs** *the same amount of work *A*,
which was performed earlier. Hence, by taking the unit charge
from infinity to the point *P* - a *new* position
relative to the repelling body - you have provided it with a
certain amount of *potential* energy. You can employ this work
relating to the point *P **as a characterization* of the point *P *of the electric
field and say: At the point *P *of the electric field
rules the *potential** A*+, whence you call *potential of a point** *the work, which must be
performed while taking the electric unit charge +1 from infinity
to the point in the field of the positively charged body.

Realize now:* You must always perform** *the same work while taking the
unit charge from infinity to *P*, *irrespectively of the path*. In fact, if this work would be larger
along the path *W*_{1} than along the path *W*_{2},
then the unit charge would return more work by returning along *W*_{1}
than along *W*_{2}. In other words, if you were to
take it along *W*_{2} *to* *P* and
then return it along *W*_{1}, you would receive
more work than you have performed, which, however, would violate
the law of conservation of energy. Hence the work cannot depend
on the *path** *to *P*, but only on the
*location** *of *P*, that is, at a
given point *P *of the electric field, the potential has
always a *definite** *value and this value is* unique*.

You can move the unit charge - we mean by this a molecule charged
with a unit charge* - to the charged body from infinity along
infinitely many paths. In Fig. 434, let the innermost curve be
the outline of the charged body and the lines leading to it the
paths, along which the unit charge can be taken to it. Say, you
take it to *B*, then you must perform a certain amount of
work *P*, that is, at *B *is the potential *P*.
If you then take it closer, say to *C*, you must perform
more work, and even more work to take it to *D*. Hence the
potential at *C *is larger than that at *B*, and
that at *D* yet larger than that at *C*. If you
release the unit charge after having taken it to *C*, it
merely is subject to the repelling force of the charged body and
therefore moves again *away* from it.

* Also in what follows, this is a test body, say, a very small sphere.

If you replace the positively charged
body - let us call it *K*
- by a negatively charged body *K*' and then again bring a
positively charged molecule to the edge of the field, *K*'
attracts the molecule towards it. We understand here by *edge of the field* the border, at which the action of the
body *K*' *effectively*
ceases - but in doing so we
remain conscious of the fact that the field *really* extends to infinity. When the charged
molecule can follow without hindrance the force, exercised on it
by *K*', it will now move from the edge of the field *inwards** *(previously, it moved outwards
to the edge). In order to return it from the point *P *of
the field to the *edge*, the attracting force of *K*'
must be overcome, that is work must be performed and indeed more
work the further the point is away from the edge. If the molecule
is again charged with a charge of +1 unit, this work is exactly
the same as the work to be performed, in order to bring the
molecule *from the edge *to the point *P*, if *K*'
were charged *positively*; it was called the potential of the
point. The contrast between the work, which we perform in each
case, is the same as if we compress a spring the one time
(overcoming the *repulsion** *between the body *K*
and the molecule), the other time (overcoming attraction) extend
a spring. The charged molecule manifests the contrast between the
two cases in that, left to itself at some point *P *of the
field, in the first case it moves to the edge of the field, in
the second case moves in the opposite direction. Relative to the
point *P*, we express the contrast by calling the
potential* *in the first case *positive*,
in the second case *negative*.

However, somewhere between +
and - lies zero. What is
the potential zero? Answer:
The potential of *Earth*. Earth is a conductor. If electricity
is taken to it, it gets charged, whence it must, like *every* charged body, attract or repel other
charged bodies, that is, have a potential. Since it is immensely
large, its potential remains unchanged however much electricity
it accepts or gives away - comparable to a heat container of
immense size, the temperature of which does not change whatever
is the amount of heat it takes in or loses. That is why you
employ Earth's potential as *zero* just as you use the temperature of
melting ice as *zero* without implying by this that the
temperature of *melting* ice is not a temperature nor Earth has
no potential. Earth's potential is used as *marker of potential*: We *call** *a
potential positive, if it lies *above*, negative, if it lies *below* it.

How do you* discover *whether
the potential of a point lies above or below that of Earth?
Similarly, how do you discover whether the temperature of a heat
source lies above or below that of melting ice? If you place the metal sphere for its
examination into a mercury bath at the temperature of melting ice
and heat flows *from the
sphere* to the mercury
(as you conclude from the rising of a thermometer in the bath),
then the temperature lies *above** *0º, and if there is no
transport of heat, the temperature of the sphere is *equal** *to that of melting ice. It is
quite similar in the case of electricity: It flows automatically
only from a higher to a lower potential; on this fact is founded
our examination of whether a given potential lies above or below
that of Earth. We have instruments which indicate whether in a
wire, which conducts electricity between two points, electricity
flows or not, that is, we can find out whether the potentials of
the two points differ or are the same; the instruments also shows
the *direction* of the flow of electricity, that is, *which* point has the higher potential. Such an
instrument also indicates whether the potential of a charged body
of a point in a field lies above or below that of Earth. However,
the potential of a given body is only rarely of interest with
respect to that of *Earth*, as a rule, only with respect to that
of another body or point in an *electrical field*, because we are always only concerned with interactions
between *charged *bodies, one of which may on occasion be
Earth. During such measurements, you use the potential of one of
the two bodies as *zero *and measure how much it lies above or
below that of the other body. It is somewhat like the case when
we are only interested in the temperature difference of two
bodies. As a rule, the temperature of a room is only of interest
relative to that of our body, that is, we are interested in the
temperature difference between our body and the room. We find its
numerical value *via *their relationships to 0º, because
that is the way thermometers work. However, differences in the
potentials between two points can be measured directly by
connecting the points with each other *via* an
electrometer. In this way you discover the difference of the
potentials, which they have relative to Earth. You use instead *potential difference** *just* **potential** *or also, if the electricity is
set in motion, *electromotive
force *(EMF)*.*

In order to state at a given
location the measure and number of a potential above or below
that of Earth, you employ the *unit** *potential.
It is for measurements of potentials what *one degree** *is for that of temperature.
The potential is work and work is measured in erg. We now define with the aid of the
concept of work the unit of the electrostatic potential: Let
there be somewhere an isolated, charged body; if the work 1 erg
is required to bring a molecule, charged with *unit *electricity, from Earth to this body,
its potential lies by *one
unit electrostatic potential** *above that of Earth; the body has then the *potential one*. In practice, you employ for
measurements of potentials and potential differences 1/300 of
this unit; it is called 1 Volt, whence the definition is: 1 Volt
= 1/300 the electrostatic unit potential.

Practical examples: The potential difference (EMF) between the poles of a galvanic element is 1 - 2 Volt. In order to make electric incandescent lamps glow, the end points of their wire must have a certain potential difference: Lamps using the electricity of large scale networks are mostly such that they require a potential difference between 200 and 240 Volt. In order to drive an electric tram, their rails and the overhead wire must have a potential difference of about 500 Volt.

All instruments for the
measurement of potential differences and direct indication of
numbers of Volt are called *Voltmeters*. Some of them employ the electrostatic
attraction or repulsion between charged bodies like the already discussed electrometers. Also the quadrant electrometer becomes
a Voltmeter, if its scale is calibrated in Volt. We will describe
roughly how this is done: Two oppositely charged, neighbouring
bodies attract each other. The magnitude of the force of
attraction depends on the magnitude of the potential difference
between the two, their form, their size and their relative
position. If they are two parallel plates like *A* and *B*
in Fig. 431 and you know their sizes and distance, you obtain from
the theory the relationship of the attractive force to the other
quantities. Let the plate *B* have 100 cm² and the
distance between *A* and *B *in the equilibrium
position of the balance be 0.5 cm. If you then charge *A*
and *B *so that *B* sinks and you must place 721
mg* on the right hand side scale dish, in order to return the
balance to equilibrium, then the potential difference between *A*
and *B* is 2000 Volt. In order to calibrate the
electrometer's scale, you now connect its housing to the one, the
aluminium leaf to the other parallel plate and when the balance
has returned to equilibrium mark on the scale 2000 Volt

**Equipotential Surfaces. Lines of
force**

As you find out, whether the potential at a
point lies above or below that of Earth, you discover that *many *points
in a field (Fig. 434) have the *same*
potential as the point *B*, that is, *many** *points
can be reached by the same effort *P.* If all these points
are linked, they form a surface, which surrounds the conductor
like a shell; similarly, you find a surface, all points of which
have the same potential as *C*, etc. Such surfaces are
called *equi-potential** *or* **level surfaces**. *Also,
the surface of an isolated conductor is a level surface, since,
according to our assumption, the electricity on it is at *rest**. *Hence all points of its surface must also
have the *same* potential, because otherwise the electricity would *flow* from
the points of higher to those of lower potential.

Level surfaces enclose each other and the
conductor like the layers of an onion; they are only mathematical
concepts, but with their aid we can understand better certain
processes in an electric field. Consider first several *general, geometrical* properties, relating to the direction and magnitude of
an electric force. Let the charged point body at *D' *(Fig. 434) move on its own. It then moves to a point
of lower potential, that is, it leaves
the level surface through *D*' and moves *outwards *away
from the conductor. But in
what direction? It aims at
any point of that level surface, which is the neighbour of *D*'
in the outwards direction (in Fig. 434, for the sake of clarity,
it is substantially away from D''). But at which point does it aim? At *a* or at *b
*or which other point?
As it is freely movable, it moves naturally in the direction of the force, which at *D*' acts on it. This
force only acts between points with *different *potentials.
Hence it can only act *at
a right angle* to the
level surface. A force, directed at an angle to the potential
surface, would have a component tangential to it (which joins
points of equal potential) and one perpendicularly to it - *this one alone is active**. *In other words: The path of
the point-body is everywhere *at right angle* to the *level
surface** *on
which the point happens to be. Fig. 434 shows such paths.
Everyone indicates simultaneously at each of its points (by the
tangent) the direction of the electric *force*, whence it is called a *line of force*. You can even make lines of force *visible*, as will be described
below.

What is the size of the
electric force perpendicular to a potential surface? In order to discover the force, which
drives a charged molecule from *D* to *C*, we
return to the definition of the potential. Let *P*_{C}*
*be the work to be performed in order to move a molecule,
charged with unit electricity, from infinity (more simply, from
the edge of the field) to *C*, and *P*_{D}*
*the larger work, in order to move it from the edge to *D*.
(Hence *P*_{C}* *and *P*_{D}*
*are the potentials at *C *and *D*.) In order
to bring the molecule after its arrival at *C* to *D*,
we must therefore in addition to the work *P*_{C}*
*perform so much work that *P*_{C}*
*becomes *P*_{D}, that is, we must do
the work *P*_{D}* *- *P*_{C};
the path along which this work is performed is of no consequence. The same work *P*_{D}*
*- *P*_{C} is now done by the
electric force on a molecule with unit electric charge as it is
driven from *D* to *C*. If it has **e**
units, the work performed by the electric force to take the
molecule from a location with potential *P*_{D}*
*to one with potential *P*_{C} is **e**
times as large, that is, **e**·*(P*_{D}*
*- *P*_{C}).

Once you have found the entire
field of level surfaces and lines of force, as in Fig.434, the
field is recorded, say, *topographically*. For example, for the point *F*,
the direction of the* **line of force** *through it indicates the direction in which
the charged point will move. Moreover: If we imagine the *level surfaces* in Fig. 434 recorded in such a way that
the values of the potentials differ by equal amounts from surface
to surface, you will understand that a molecule, in order to
cover the same potential difference, need only cover shorter
distances when near the conductor than when it is further away
from it. On a map, this would mean that the *gradients** *differ at different locations.

If you compare a charged
conductor with a source of heat, the level surfaces are matched
by the isothermal surfaces surrounding a heat source: There
corresponds to each surface a *definite**
*temperature, for each of its points the same, but from
surface to surface another temperature; on surfaces closer to the
heat source, it is higher than on those further away; lines,
which are perpendicular to each surface, tell at each location
the *direction** *of the heat flow and the
distance (measured along this line) between two of them, between
which there is a temperature difference of 1º, measures the
gradient.

It is quite difficult to find the level surfaces and lines of force in particular cases. We will only explain their form by means of two simple examples.

Let the conductor be a *positively charged sphere* (Fig. 435) and the field around it
extend to infinity. We approach it with a positively charged
molecule radially as far as *P*. We must then perform
work, the magnitude of which is measured by the potential at *P*.
We would have had to perform the* same work*,
if we had taken the molecule to the conductor along another
radius to the same distance. This means: The same potential,
which applies to *P*, applies to all points which have the
same radial distance from the sphere as *P, *that is, lie
on the *spherical
surface *about *C*
with radius *CP*. This surface is the *equi-potential** *or *level surface*. Obviously, *every** *spherical surface about *C *is
such a surface. But on each of them the potential differs: On the
surface *R, *it is *smaller
*than on the surface *P*,
but on the surface *Q* it is larger than on the
surface *P*, since less work is required to take a
molecule to the distance *CR *than* *to the smaller
distance *CQ *from the centre of the sphere. The lines of
force are equally clearly laid out: They are *perpendicular* to the level surfaces - here spherical
surfaces; therefore the lines of force are the radii of the
spherical surfaces.

How large is the potential at a
given point? Let** e**
electricity units be distributed uniformly over the surface of a
sphere. Then a computation tells us that the potential at a point
of the field, the distance *a* of which from its centre is
larger than the radius of the sphere, is **e**/*a*.
The meaning of this number is: In order to bring a molecule,
charged with the positive unit of electricity, from an infinite
distance from the sphere, charged with **e**
positive eletricity units, to the distance *a* from the
centre, you require the work **e**/*a* erg.
If, as earlier, the charge is **e***=*12
electricity units and the radius of the sphere is 1 cm, you must
perform the work 12/10 erg while taking the molecule to 10 cm
from the *centre *of the sphere, that is, the point which
lies 10 cm from the centre of the sphere has the potential 12.
Similarly, we find that at the

distance of | 9 | 8 | 6 | 4 | 3 | 2 | 1 | cm from the sphere's centre | ||||||||

the potential is | 1.33 | 1.50 | 2.00 | 3.00 | 4.00 | 6.00 | 12.00 |

Two equally strongly,
oppositely charged bodies *A* and *B* are of
special interest; their fields *intercept*
each other. If the amount of electricity is known, you can *compute* for every point in the field at given
distances from *A* and *B* its potential in the
field *composed** *of the two fields.We will now
perform the calculation and construct the potential surfaces. Place a horizontal
plane through *A* and *B* - the plane of the
drawing of Fig. 437. It intersects the field as well as the
potential surfaces, whence there arise certain curves - the solid
curves 1, 2, 3, etc. All the points on 1 have the same potential,
similarly those of 2, etc. If positively charged molecules travel
from *A*, they will move away from *A*, the point
with maximum potential, to points of lower potential until they
arrive at the point of minimum potential, the point *B*;
in doing so, they move along the *lines of force* - the dotted lines of Fig. 437 (they intersect the
individual equip-otential curves at right angles).

You can make these
lines of force *visible*. Let *A* and *B* be small steel spheres,
fitted into a (very clean and dry) mirror glass plate and linked
to an electrifying machine. Charge them to a corresponding high
potential difference and cover the plate with very fine, dry
gypsum powder. If you then shake the powder by gently knocking
against the plate, the gypsum crystals arrange themselves along
lines similar to the dotted lines of Fig. 437 (magnetic lines of force)..

We have only spoken of *positively** *charged molecules, however, a
negatively charged molecule, starting from *B* or taken
anywhere in the field and then left to itself, moves naturally
along the same lines of force, but in a direction *opposite* to that of the positively charged
molecule; for negatively charged molecules, the largest potential
is at the negatively charged body *B*; it decreases along
the lines of force towards *A*.

Since a charged body moves always from a
higher to a lower potential (*downhill*),
you know now the condition under which two charged bodies move
towards one another or move away from one another. Let *A*
and* B *in Fig. 437 be again two equally charged
molecules, say, positively charged. In order to bring a molecule,
charged with 1 electric unit, to the body, you must obviously,
whether you do so from *y* or *y*', perform more
work than from *x* or *x*'. Hence follows: The
potential is largest between *A* and *B, *it *grows** *in the direction of *x*
and* x*' towards the two bodies. If you make *A*
and *B *sufficiently easily movable and leave them to
themselves, they will move, since they then move *downhill *towards *x* and* x*',
whence they move away from each other - we *say *that they repel each other. If *A*
and *B *have *opposite*
charges, the potential
values of both the fields around *A *and *B *decrease,
but both move most strongly towards the centre between *A*
and *B*; on the line *yy*', the potential is 0,
which means that the fields drop *towards this line* much more strongly than outwards. If you make again *A*
and *B *sufficiently movable, both of them will move
there, and we say: They attract each other. - *A *and *B
*behave like two masses, which are placed on a curved track
(Figs. 438 a, b) and then are allowed to react to gravity: Both
of them move downhill, the one time away from each other, the
other time towards each other.

**Electrification by
induction**

Before Faraday, the fact that two bodies move towards or away from
each other due to their electrification was viewed as an *action at a distance** *in which the medium *between** *the two bodies did not *participate**. *This view was supported by
the fact that one only had to bring an electrified body *near** *to a not yet electrified,
easily moved body, for example, one in pendulous suspension, in
order to move it. The observation (Thales of Miletus 640-550 BC)
that amber, when rubbed with a dry cloth, attracts almost
weightless particles like bits of cork, is considered to be the
longest known electrical phenomenon.

Accordingly,
an electric body seems even to act on a* **not** *electrified body at a distance. However, the
motion actually takes place as follows: At first, the not
electrified body is *also** *electrified, namely by the *approaching** *electrified body - one says *by induction* - and *then** *both
attract each other. Thus we have the stages: **1. ***Electrification** *as action *at distance* and then **2.** *Mass motion* as action *at distance*. Fig. 439 shows a basic experiment. An uncharged,
isolated conductor *A*, a brass cylinder on a glass foot -
at its ends electrified pairs of pendulums - is taken* *to
the charged sphere *B. *You then observe:

**1.** Both
pendulum pairs spread out, that is, both ends of the conductor *A*
are charged. **2.** The pair *further away* from the sphere indicates
presence of the same type of charge as that of the sphere, the
pair *closer by* an opposite charge. In brief: The
conductor *A* carries at its ends opposite charges. **3.** The spreading of the pendulums becomes
smaller, the closer they are moved to the centre of the cylinder
and vanishes at certain points of the cylinder. The totality of
these uncharged points around the centre of the cylinder forms
the *neutral line*. **4. **If you remove or
unload the sphere, the pendulums collapse, the cylinder becomes
again unelectric, whence the two opposite charges had the same
size. **5****.** If you discharge the cylinder to Earth at either end,
the pendulum pair at *b* collapses, that is, its charge,
which is equal to that on the sphere, *vanishes*. The other charge remains; it is *bound* by *induced *electricity.
**6.** If, after discharging the cylinder, you
remove the sphere first of all, the pendulum pair *b*
spreads again, and indeed with the same charge as the pair *a*.
Hence now the *entire** *surface of the cylinder is
charged oppositely to the charge on the sphere. **7.**
If several conductors are lined up (Fig. 440), each behaves like
that next to the sphere.

Induction also occurs, if you
place between the induced body *e* and the induced body *ab
*a glass plate *d *(Fig. 442). In fact, it occurs
through every isolated body, be it solid, fluid or gas, that is
also through the atmospheric air.

If you electrify a glass sphere
*M* positively and then take it close to an unelectric,
suspended, small body *N*, it becomes to start with
electric by induction. The charge of the glass sphere attracts
more strongly the negative electricity *a* of the induced
body due to its shorter distance from *N* than *repelling* the further away positive charge *b*;
this is why the glass *attracts** *the body. During the following
contact, a corresponding quantum of the positive charge of the
glass sphere neutralizes the negative charge of the body. The
excess positive charge on the glass has now only to deal with the
positive charge of the induced body, that is, it *repels therefore the body** ab*. You can see this
attraction and subsequent repulsion when you rub sealing wax or
hard rubber with wool and then bring it close to paper clippings
or similarly easily moved particles.

The fact that the electric
pendulum (cf. **3.
**above**)
***does not* spread *equally*
strongly at all points of the cylinder indicates that the charge
is not the same at all points. It is largest at the ends of the
cylinder, zero on the neutral line and has intermediate values in
between. In this sense, you speak of *density *of
electricity at a point. Despite of the variability of the
density, the electricity is at rest on the surface of the
cylinder after the positive and negative electricities have
separated; this is a proof that at all points of the surface the *potential* is
*equally large*. At
first, this circumstance comes as a surprise: For example, the
point *B* in Fig. 439 above, although the *density* of the electricity at it vanishes, is
to have a *non-zero** *potential, that is, it is to
demand work to bring a molecule, charged with a positive electric
unit, into its vicinity, although it does not hold a charge. You
should take into account the fact that its neighbours are
charged, whence they repel molecules and *themselves *demand work as the molecule approaches *P*.

In general, also on a segregated, charged body, the electricity density differs from point to point. The shape of the body is decisive: A sphere has everywhere the same density on its surface, a cylinder has larger density at its ends than in its middle, a disk's density is greater at the edges than at the centre of its faces, a cone's density is stronger at the rim of its mantle than on its sides, but is greatest at its tip. In general: The electricity density on a body is greatest where it has the largest curvature.

A sharp point occupies a special position. Due
to the large density of electricity at a vertex, the air there *conducts*,
whence electricity passes
directly on to the air molecules, which then, repelled by the
equally charged tip, move away. Their positions are occupied by other molecules, so that the
cusp loses all the time electricity and maintains around it
motion of the air. This air circulation can become a distinct
wind (Fig. 443a). However, a vertex also *charges*.
If you take a charged, pointed body *A *(Fig. 443b) very
close to a charged body *B*, the stream of air discharges
its charge on to a body without charge, so that *A* is
unloaded, *B *is charged. In contrast, if you take a
pointed body without charge *A*' close to a loaded body
(Fig. 442 c), negative and positive electricity is generated by
induction. Negative electricity flows from the point to the body *B'*
and gradually unloads it; in the end, there is only positive
electricity on *A*', that is, it is as if the charge of *B*'
were simply transferred to *A*'. You say: The vertex has *sucked in *the
charge. The suction action of a sharp point supports also the
action of lightning
rods.** **The suction is
so strong that it is occasionally employed technically. For
example as follows: You can charge with electricity, generated by
rubbing of a glass plate, another
body, if you take it away from the glass plate to the body, as
soon as the electricity is formed. You employ the method of John
Tyndal 1820-1893 (Fig. 444). Attached to the silk *R* -
the rubbing c*loth* - is a small copper or brass strip *P. *During
rubbing (Fig. 445), the side facing the glass is covered with
fine needle points, so that the glass tube is surrounded by a
ring of spikes. As you rub with the silk cloth, the ring of
spikes glides all the time on that part of the tube to and fro,
which had been touched by the silk and just been separated, that
is, it has been charged positively. The spikes suck in the
positive electricity, which reaches *B *through the wire *W*
. (Application in electrical machines )

**Bondage and re-bondage of
Electricity by induction**

Your *first impression** *is that also electrification
by induction is an action *at
distance*. But if the
charge on *B *(Fig. 439) really acted on *A **without mediation*, that is, *A *charges without
participation of something else but for *A* and *B*,
it would have to be immaterial what fills the space in between
them. But the medium between them has a very important role. In
order to understand this, we return to the earlier discussed phenomenon 5.

Let the negative charge, induced on the body *A
*by the positively charged sphere *B*, be so strongly
bonded, that it does not even depart as *A* is earthed,
that is, only its positive electricity leaves. We will now focus
our attention on this bonding of electricity by induction.

*Bonding *is always *reciprocal*. Hence *induced
*electricity influences also the
electricity which induces. The force, which the induced conductor
exerts *outside*, for example, the repulsion of +1 unit of electricity,
which is brought near it, becomes thereby much weaker than it was
initially. In other words: Its potential has decreased. It must
again accept electricity before its potential returns to its
initial value; it thus becomes a *collection apparatus *(a condenser): Let a
source of positive electricity be kept throughout (by any means
whatever) at a constant potential, also when it loses
electricity. Connect the conductor *A* to it (Fig. 446);
then positive electricity flows to *A *through the
conducting connection until *A *has the same potential as
the source of electricity. Now let *A *approach* *the
conductor *B*. The positive electricity on *A*
binds the negative one on *B*; we now *earth* the
positive charge. Since a part of the positive charge is *re*-bonded
to *A*, the potential of *A *drops and again new
positive electricity can flow to *A*. The newly entered
electricity generates again in *B* negative electricity to
one side and repels positive electricity to the other side. If
this repelled electricity is again earthed, the process of
bondage and re-bondage is repeated. The potential of *A*
sinks again and *A* must take in again electricity, in
order to raise its potential to the initial level.

However, this cannot continue indefinitely. Not
all of the electricity of *A* becomes outwardly actionless
by re-bondage - only one part. The remainder stays free, whence
during every new connection of *A* to a source of
electricity the amount of *free
*electricity on it increases and
eventually *A* attains its former potential, *although**
*it binds the electricity of *B*. Then *A *holds
more* **electricity** *than before, although its *potential* is the same. If you move again *B*
to a larger distance from *A*, the hereto bonded
(or better: *re*-bonded) electricity is freed and the
potential of *A *increases. In this manner, a conductor
can be charged to a potential much higher than that of the source
of electricity, which causes the charge.

For example, this method is
employed, in order to reinforce the potential in the gold leaf
electroscope (Fig. 447), which otherwise would not be indicated
at all or only vaguely. You fix to the bar *l* with the
gold leaves the metal plate *N*, cover it above with a
layer of varnish and place on top of it a second metal plate *M
*with an isolated handle. You then connect *N* to the
source of electricity and earth *M *(Fig. 447 left hand
side). You have then the set-up of Fig. 446, which explains the
bondage and accumulation of electricity.* *Here *N *corresponds
to the conductor *A*, which is linked to the source of
electricity, *M* to the conductor *B*, in which the
electricity is generated by induction, in spite of its being
earthed, and the varnish layer between *N* and *M*
to the layer of air between *A* and *B*. If you now
separate *N* from the source of electricity and take away *M*,
the entire electricity* *linked in* N *is freed and
acts on the gold leaves the more, the larger is the area of the
two metal plates and the thinner is the layer of varnish.

**Dielectric as bearer of the
electric field**

If the plate *A*
in Fig. 446 is loaded to a given potential *V*, while only
*air *separates it from *B*, it accepts
a certain amount of electricity. If you then fill the space
between it and *B* with paraffin or glass or any other
insulating substance, it will accept a larger amount of
electricity than before, in order to attain the same potential.
These observations guided Faraday
away from *action at a distance *of electric forces to new views of the
nature of induction.

He started from
his insight that a magnetized bar, which is broken into two
pieces, always yields two new magnets, *each** *with a North pole and a South
pole (Fig. 448). You can conceive that the entire magnet *NS*
consist of small magnets *ns*, whence the magnetisation of
a piece of iron is eventually reduced to its single *molecules**. *Faraday then
assumed that due to the electrification of the conductor there
arises in the bounding insulator- he calls it *dielectric *- an electric state, because there form
similarly in the molecules of the insulator positive and negative
poles, which on their part act on the adjoining conductor (Fig.
449).

Let *A *be a positively,
*B* a negatively charged conductor and *ab* a row
of molecules of the insulator between *A* and *B*.
Once the poles in the molecules have formed - Faraday calls this
state *dielectric
polarization **- *pairs of
neighbouring molecules in the same row turn towards each other
opposite poles and attract each other and the ends *a* and*
b *attract *A* and *B. *Thus, as a result of
its polarization, the rows of molecules *ab* form of a
band, which tends to contract and bring the electrified bodies *A*
and *B* closer together; every other row of molecules
between *A* and *B *does the same. Hence there
exists a tendency to contract in the direction AB.

The state of tension, into which an insulator enters, is a main property of the electric field. The lines, along which the polarized molecules of the insulator contract each other are nothing else but the lines of force, along which a freely movable, charged molecule moves in an electrical field. As a rule, these lines of force are not straight, but more or less curved. Moreover, it is of no consequence whether the space between the two conductors is occupied by air or another (solid, fluid or gaseous) insulator. All these ideas took Faraday away from the concept of direct action of electric forces at a distance; he replaced this concept by a theory, according to which action of a force is transferred by dielectric polarization of the intermediate medium. He employed the words:

"Here the most important
among the deductions from the concept that induction is a
molecular process is the suspected action along *curved lines*, for if this could be uniquely established, I cannot
see how the old theory of sole action along straight lines at a
distance could be maintained or how the conclusion that ordinary
induction is an action between adjacent particles can be
rejected." Moreover, he wrote: "One can conceive by
means of lines of force the external force, which starts from an
electric body and reaches into the distance. The lines or the
forces, which they represent, remain conserved as long as they
are inside of or penetrate an insulating medium. They propagate
until they encounter a conducting substance, on which they excite
an equally large state, which is opposite to that of their source
and of equivalent degree, and in this way their insulation finds
a border or they continue, if no such body is present."

Faraday proved over and over again by new facts: During
polarization, the dielectric is decisive, the conductor has only
the role of the *border
of the dilelectric*. *Inside*
the dielectric, the positive charge of one molecule neutralizes
the negative charge of its neighbour on the line of force. Only
when the dielectric reaches a conductor, the charge is detected -
the *charge of the
conductor*. In a line of force, for
example, in the row of molecules *ab* (Fig. 449 above),
the starting point on the conductor *A* and its end point
on the conductor *B* signify *charges*, and indeed *corresponding** *points.

**Modern ideas of the nature of
dielectric polarization**

Today we view (on
the basis of substantially extended knowledge of electric
processes) electricity as something *corpular*;
we ascribe to it atomic structure and assume existence of
positive and negative elementary particles of a definite size.
According to this concept, the positive (negative) *charge *of the conductor *A* (*B*)
(Fig. 449) is identical to a layer of
positive (negative) elementary particles on its surface . The end points of the lines of
force, linking opposite charges, carry accordingly on the one
hand positive and on the other hand negative particles.
Elementary particles can be considered to be two elements - we
denote them by and
- with which other
elements can *bond** *(some with , others with , for example, the compounds *H* and *K* - a hydrogen ion and a
potassium ion -, the compounds Cl - a chlorine ion -and write them, in
order to distinguish them from uncharged atoms *H*^{+},*Cl*^{-}.
etc.), but which can also bond with each other into - a neutral particle.

According to the view of the
structure of matter in 1935, its atoms consist of positive and
negative elementary particles; an atom is *not*
charged, if the sum of the positive elementary charges equals the
sum of the negative ones. However, if the particles are separated
from each other, as Fig. 449 indicates (dipole), then there
occurs inside the dielectric that state of tension, which we have
described above, and on the bounding layer forms a free charge.

Note one more point: The end
points of an *electric* line of force differ physically completely, that is the
positive elementary particles are something completely different
from the negative ones. This is not so in the case of *magnetic** *lines
of force . Their end points - the
positive and the negative poles - only differ in that their *actions*
have different signs.