venient means for producing these large e. m. f.'s is by means of
the electrical machine, several forms of which are described in
subsequent articles. In all diagrams, however, a battery will be
shown where it is desired to indicate an e. m. f.
24. Mechanical analogue of charged bodies. Consider two
cavities A and B, Fig. 10, in an elastic solid, jelly, for example.
. If the cavity A is expanded,
for example, by forcing air
into it, and the cavity B con-
tracted, the surrounding jelly
will be stressed, the lines of
stress being somewhat as in-
dicated in the figure. It is
not worth while to examine
minutely into the stressed
condition of the jelly in this
case inasmuch as this stress
is not completely analogous
to electrical field. This mat-
ter is taken up again in Chap-
25. The electric discharge. When charged bodies loose their
charge they are said to be discharged. Many important and
interesting phenomena accompany this discharging of bodies.
These phenomena are described in Chapter X. For the purpose
of the present discussion it is sufficient to note, that charged
bodies when left to themselves always loose their charge more or
less rapidly so that in electrostatic experiments charged conduc-
tors must be thoroughly insulated ; and that two charged bodies,
for example A and B, Fig. 9, loose their charges almost instan-
taneously when they are connected by a wire, and of course the
electric field disappears at the same time. A line of force never
begins and ends on the same conductor nor upon two conductors
which are brought into contact or connected by a wire.
26. Electric charge resides wholly on the surface of a charged
conductor. Electrical screening. The electrostatic phenomena
exhibited by the charged conductors A and B, Fig. 9, are pre-
cisely the same whether the bodies are solid or hollow ; and, if
the bodies are hollow, not the slightest effect of the charges can
be detected inside of them, however thin their walls may be.
Tlic lines of force of the electric field end, therefore, at the surface of
the charged conductors or, as it
may be said, the electric charges
reside wholly on the surfaces of
A conducting shell (for ex-
ample a metal box) screens its
interior completely so that no
action of any kind reaches the
interior from charged bodies out-
side. Thus a shell of metal C,
Fig. 11, screens its interior com-
pletely. The lines of force which
touch the shell C end at its sur-
face. The ending on C of the lines of force from A is negative
charge, and the beginning on C of lines of force which reach B is
The fact that electrical field does not penetrate into a conductor
shows that conductors cannot sustain the peculiar kind of stress
which constitutes electrical field and therefore this electrical stress
cannot be transmitted from the outside to the inside of a metal
27. Mechanical analogue of electrical screening. Consider a
solid body B, Fig. 1 2, entirely separated from the surrounding
solid by the empty space cee. Stress and distortion of the sur-
ELEMENTS OF PHYSICS.
rounding solid cannot affect B in any
way and, conversely, stress and distor-
tion of B cannot affect the surrounding
solid, for the empty space is incapable
of transmitting the stress. This empty
space in its behavior towards mechanical
stresses is analogous to a conductor in
its behavior towards electrical stresses
28. A charged conductor shares its charge with another con-
ductor placed in contact with it. Fig. 1 3 shows the lines of force
in the neighborhood of a charged conductor A. When another
conductor B is placed in contact with A the lines of force arrange
themselves as shown in Fig. 14. The charge which was initially
on A spreads over both A and B as shown by the ending of the
lines of force.
29. Faraday's experiment. A charged body B is lowered into
the interior of a metal vessel and the opening of the vessel is
closed with a metal lid. As the body is lowered into the vessel,
each line of force emanating from B is cut in two, as it were, by
the wall of the vessel so that when B is entirely enclosed by the
vessel as many lines of force emanate from the external surface -of
the vessel as from the body B and all the lines of force which ema-
UNIVERSITY OF CALIFORWA
DEPARTMENT OF PHYSICS
ELECTROSTATICS. ' 23
Httte from B end on the internal surface of the vessel. Therefore
if Q is the amount of charge on B, the amount of charge on the
inner surface of the vessel is Q and the amount of charge on
the outer surface of the vessel is Q. Fig. 1 5 shows the state of
the electrical field while the body B is being lowered into the
vessel and Fig. 16 shows the state of the electrical field when the
body B is enclosed by the vessel and its lid.
Further, the distribution of the electric field outside of the
vessel does not depend in any way upon the position of the body
B inside of the vessel. Thus, in Figs. 16 and 17 the distribution
of the electric field (lines of force) is very different inside while
the external field is the same. If the body B (a conductor) is
brought into contact with the wall of the vessel, the charges on
the body and on the inner surface of the vessel disappear, while
the external field is not affected, as indicated in Fig. 1 8.
30. Giving up of entire charge by one body to another. When
the body B, Figs. 15, 16, 17 and 18, is lowered into the vessel
and allowed to touch the interior it looses all its charge and re-
mains without charge when removed from the vessel, while the
charge left on the outside of the vessel is equal to and of the
same sign as the original charge on B. The body B may thus
be said to give up its entire charge to the vessel.
ELEMENTS OF PHYSICS.
31. Charging by influence. Let A, Fig. 19, be a charged
body. The neighborhood of A is an electric field. Let B be a
conductor brought near to A. This body B takes on positive
and negative charges where the lines of force end upon it as
shown. If a third conducting body C is brought into contact
with B as shown in Fig. 20, then B and C are charged as in-
dicated in the figure, and the bodies B and C retain these charges
when they are separated and removed to a distance from A.
This operation is called charging by influence ; equal amounts of
ELECTROSTATICS. 2 5
positive and negative charge being produced. It often occurs
that one wishes only to charge the body B, in which case the
hand may serve instead of the body C.
32. Charging by contact and separation. Many substances
when separated after intimate contact are found to be highly
charged. Thus silk and glass when rubbed together and sepa-
rated are charged, the glass positively and the silk negatively ;
fur and rosin when rubbed together and separated are charged,
the fur positively and the rosin negatively. This charging by
contact and separation is made use of in the so-called Frictional
electric machine. Charging by contact and separation is more mi-
nutely discussed in a subsequent article.
33. Electroscopes, A device for indicating the existence of
an electric charge or of an electric field is called an electroscope.
T/ie pith-ball electroscope. Electric charge on a body AA, Fig.
21, may be indicated by hanging from the body a light ball of
pith as shown. The pith ball takes part of the charge of the
body and the lines of force emanating from the ball pull it into
the position shown. A suspended pith ball which has been
(positively) charged is pulled in the direction of the lines of force
ELEMENTS OF PHYSICS.
when placed anywhere in an electric field ; this affords an easy
means for tracing the lines of force. The pith ball used as an
electroscope is usually gilded, making it a conductor, so that it
may be easily charged and discharged.
The gold-leaf electroscope consists of a metal disk D and rod
R, Fig. 22, from the lower end of which two gold leaves are
hung side by side. The whole is supported in a glass case cc
which protects the gold leaves from air currents. The sides of
cc are lined with strips of metal foil ff to increase the sensitive-
ness. When the disk, rod and gold leaves are charged the leaves
are pulled apart by the lines of force as
shown in Fig. 23, which for clearness,
shows the instrument without a glass case.
The action on- the gold-leaf electro-
scope, of a charged body brought near to
the plate D is briefly as follows :
(i) When the electroscope has no initial
charge some of the lines of force pass from
the body into the disk and then out from
the leaves to the strips ff, causing the
leaves to diverge. If the body is removed
the electroscope again becomes neutral.
If, while the charged body is near D, the disk or rod is touched
with the hand the lines of force passing out from the leaves
cease to exist and the leaves fall together. If now the charged
body is removed the lines of force going into the disk from the
charged body spread over disk, rod and leaves, the leaves diverge,
and the electroscope is left charged.
(2) When tJic electroscope lias an initial charge, say a positive
charge, then a positively charged body brought near to D pushes
the initial charge down into the leaves, as it were, and the diver-
gence of the leaves is increased. If a negatively charged body
is brought near to D the positive charge is pulled up into the
disk, as it were, and the divergence of the leaves is decreased.
If the negatively charged body is brought nearer, the leaves will
come together ; and if the body is brought still nearer, the leaves
will again diverge.
This action of a charged body upon a gold-leaf electroscope
affords a convenient means for detecting and identifying positive
and negative charges.
34. The electrophorus and electrical machines. See text -book,
Arts. 438, 439, 440, 441, 442, and 443.
35 The condenser. Electrostatic capacity. Consider two par-
allel metal plates AB, Fig. 24, separated by air and connected
through a ballistic galvanometer to the terminals of a battery as
shown. When the connection with
the battery is made electric charge
rushes through the wire into the
plates as described in article 23. The
quantity of charge which thus rushes
into the plates, and which may be
measured by the ballistic galvano-
meter G, Fig. 24, is strictly proportional * to the e. m. f. of the
battery. That is
in which Q is the quantity f of electric charge which is pushed
into a pair of insulated plates by an e. m. f., E, and J is the pro-
* An experimental fact.
f The quantity which is on one plate.
28 ELEMENTS OF PHYSICS.
portionality factor. This arrangement of metal plates is called a
condenser, and the factor J is called the electrostatic capacity or
simply the capacity of the condenser. When the dielectric be-
tween the plates of a condenser is air, the condenser is called an
Remarks : The charge which is pushed into any pair of bodies,
as for example A>, Fig. 9, is proportional to the e. m. f. so that
equation (5) is entirely general, and any pair of bodies constitutes
Units of capacity. A condenser is said to have one farad of
capacity when one coulomb of charge can be pushed into the
condenser by an e. m. f. of one volt ; J in equation (5) is ex-
pressed in farads when Q is expressed in coulombs and E in volts.
The farad is very large compared with the capacities of conden-
sers met with in practice, therefore the micro-farad (one millionth
of a farad) is a more convenient unit.
When, in equation (5), Q is expressed in c. g. s. units charge
and E in c. g. s. units e. m. f.,y is expressed in c. g. s, units
capacity. The c. g. s. unit of capacity is equal to io 9 farads.
The Ley den Jar is a condenser made by coating the inside and
outside of a glass jar with metal foil.
36. Hydrostatic analogue of the condenser. Consider a chamber
with water-tight compartments, A and B, Fig. 25, separated by
^ B^M - an elastic diaphragm DD of rubber. If a
pump P is connected to the compartments
as shown a definite quantity of water Q will
be forced through the pipe out of one com-
partment into the other and this quantity
will be proportional to the difference of
pressure E generated in A and B by the
pump. That is
FIG. 25. Q=J (5) bis
in which J is the proportionally factor. The diaphragm separat-
ing A and B is subjected to mechanical stress very much as the
insulator or dielectric between the plates of a condenser is subject
to electrical stress.
37. Measurement of capacity. The capacity of a condenser
may be determined by measuring with the ballistic galvanometer
the charge which is pushed into the condenser by a known e. m. f.
The capacity may then be calculated from equation (5).
In article 47 an equation is derived expressing (in new units)
the capacity of an air condenser in terms of distance and size of
the plates. Capacities of air condensers may be calculated from
38. Inductivity of dielectrics. The insulating substance be-
tween the plates of a condenser, or between any electrically
charged bodies is called the dielectric. The capacity of a con-
denser (given size of plates at given distance apart) depends upon
the dielectric. The quotient : capacity of a condenser with given
dielectric divided by its capacity with air between its plates is called
the inductivity^ of the dielectric. For example, the inductivity
of kerosene is 2.04 ; that is the capacity of a condenser is 2.04
times as great with kerosene between its plates as it is with air
between its plates. A table, page 141 text-book, gives the in-
ductivities of a few substances.
39. Work done in charging a condenser. When an e. m. f.
E is connected to an uncharged condenser, the work EQ done
by the e. m. f. as the condenser is charged is in part dissipated
because of the rush of charge into the condenser which is fol-
lowed by a surging of the charge back and forth. In order that
the whole work done by an e. m. f. in charging a condenser may
be used in forcing the charge into the condenser without any dis-
sipation, the e. m. f. must have a value zero when it is connected
to the condenser and be made to increase slowly in value. The
work done in charging a condenser in this way is all represented
in the potential energy of the charged condenser. The potential
energy W of a charged condenser is
* Sometimes called specific inductive capacity.
ELEMENTS OF PHYSICS.
Proof: Let q (= Je} be the charge in the condenser when
the growing e. m. f. has reached the value e, and let A^ be the
additional charge which is pushed into the condenser by a slight
increase of the charging e. m. f.; then A W= e-&q is the work
done in producing this increase of charge ; but e -j from equa-
tion (5) so that
Integrating this expression from q = o to q = Q we have
The equations (7) and (8) are obtained by writing JE for Q
andJ 2 2 for Q 2 , respectively, in equation (6).
40. Electric field and its intensity.
Transference of charge by a moving
ball. Consider a condenser AB, Fig.
26, with a metal ball suspended be-
tween its plates as shown. When the
condenser is charged with high e. m.
f. this ball vibrates back and forth,
-^. striking one plate and then the other,
/ \ and each movement of the ball trans-
l I fers a definite charge q from plate to
- - Illlllllllllllllllllll- 11 ^ 1 ^^ plate. The work done on the ball by
the force F pushing it across from
plate to plate through the distance x
is Fx and this work is furnished by the battery as it replenishes
the charge. The work done by the battery is Eq. Therefore,
Fx = Eq or
ELECTROSTATICS. 3 1
Any region in which a charged body is acted upon by a force *
is called an electric field and the intensity of an electric field at a
point is the factor which, multiplied by the charge at that point,
gives the force acting on the charged body. Comparing this
statement with equation (9) we see that the intensity / of the
electric field between the plates of the condenser is
in which E is the e. m. f. between the condenser plates, and x is
the distance of the plates apa
we have the general equation
the distance of the plates apart. Writing/ for - in equation (9)
in which F is the force acting upon charge q, when the charge
is placed at a point in an electric field, and / is the intensity of
the field at the point.
The direction of an electric field at a point is taken as the di-
rection of the force which would act on a positive charge placed
at the point.
See Arts. 341 to 344 of the text-book for statements con-
cerning magnetic field which hold for electric field.
41. General Relations between electromotive force and Electric
Field. Consider two conductors A and B, Fig. 27, charged by
a battery of e. m. f. E connected as shown. Suppose that an
amount q of charge is transferred from A to B along the path
pp f . The work done by the battery in replenishing the charge is
W=Eq, (4) bis
and this is equal to ike work done by the forces with which the
electric field acts upon the charge while the charge is passing along
* That is a force which depends upon the charge, and does not exist when the
body has no charge.
32 ELEMENTS OF PHYSICS.
the path. Consider an element A^ of the path. Let / be the
field intensity at this element and e the angle between A-? and /,
see figure. Then qf is the total force acting on the charge q as
it is passing along the element A^, qfcos e is the resolved part
of this force in the direction of the element, and gfcos e . A^ is
the work done by this force as the charge moves over the ele-
ment. Therefore, the total work done by the electric field upon
the charge q as it is carried from / to/' is W= Iqfcos e . A^ or
W= qlf cos e. AJ (12)
Comparing this with the equation W ' = Eq (4), we see that
the e. m. f. along a given path in an electric field is
E= If cos e. AJ. (13)
That is, each element of the path being multiplied by the re-
solved part parallel to the element of the electric field intensity at
the element, the sum of these products is the e. m. f. along the
path. The equation / == (10) or = fx as applied to the
electric field between parallel plates is a special case of equation
42. Electric Potential, The e. m. f.* between two points in an
electric field is called the difference of potential* between those
points. If a point or a region (for example the earth) be chosen
arbitrarily as the region of zero potential then the electric potential*
at a point may be defined as the e. m. f. between that point and
the arbitrarily chosen point or region of zero potential. Electric
potential is in some respects analogous to hydrostatic pressure
and is often spoken of as electric pressure.
Surfaces of equipotential. The e. m. f. is zero along a path which
is everywhere perpendicular to the lines of force of an electric
field. Therefore the potential has the same value at all points of
such a path. Similarly the potential has the same value at all
points of a surface -which is everywhere at right angles to the lines
of force; such a surface is called an equipotential surface. The
*When the e. m. f. between two points is not the same for different paths con-
necting" t the points then one cannot speak of e. m. f. as a difference of potential. This
matter is fully discussed in Chapter I. of the text- book.
34 ELEMENTS OF PHYSICS.
lines of force in an electric field touch the surfaces of conductors
at right angles, as has been pointed out in article 23, so that the
potential has the same value over the entire surface of (and
throughout) a charged conductor.
The heavy lines in Fig. 28 show the approximate trend of the
surfaces of equipotential in the region surrounding two charged
spheres, the lines of force are marked by the arrow heads. In
the neighborhood of an isolated charged sphere the surfaces of
equipotential are spherical surfaces concentric with the charged
43. Electric strength of dielectrics, Electric stress. When the
e. m. f. between two parallel plates is increased, a value is eventu-
ally reached which breaks down or ruptures the dielectric and
allows the charge on the plates to pass in the form of an electric
spark. The value, E, of the e. m. f. for which this break down
occurs is, for a given dielectric, proportional* to the distance x
between the plates. The e. m. f. per unit thickness (e. m. 1., divided
by distance between the condenser plates) required to rupture a
dielectric is called the electric strength of the dielectric. This e.
m. f. per unit thickness, , is, by equation (10), the electric
field intensity between the plates, so that a dielectric is broken
down by an electric field of a certain intensity. Electric field may
therefore be looked upon as a kind of stress.
The table on page 152, text-book gives the electric strengths
of a number of dielectrics.
44. Electric Flux. The product of the intensity o an elec-
tric field into an area at right angles to the direction of the field
is called the electric flux across the area. That is
* When any two bodies, as ^ and , Fig. 9, are charged a by an increasing e. m. f.,
the dielectric breaks down when the e. m. f. reaches a certain value, but the e. m. f.
required to produce rupture is proportional to the thickness of the dielectric only in
case of parallel plates.
ELECTROSTATICS. 3 5
in which N is the electric flux across area a at right angles to a
field of intensity/. The unit electric flux is the flux across unit
area at right angles to unit field. This unit flux is called the
line. See articles 5 and 6 of this pamphlet for statements con-
cerning magnetic flux which hold for electric flux as well.
The electric flux across an extended surface in an electric field cannot be expressed
as the product of the field intensity into the area of the surface as in equation (14),
for the reason that the field will in general vary in intensity from point to point and
also for the reason that the field may not be at right angles to the surface at every
point. In this case we have
yV=2/. cose. AS (15)
in which AS is an element of the surface, f is the field intensity at the element,
/cose is the resolved part of/" perpendicular to AS, and/" cos e. AS is the flux across
45. Dependence of the capacity of an air condenser upon size
and distance of plates. The capacity, J t of an air condenser is
proportional to , where a is the area of one plate and x is the
distance between the plates. That is
J=C- x (16)
in which C is a constant. When J is expressed in c. g. s. units
capacity, a in square centimeters and x in centimeters the ex-
perimentally determined value C is where v= 3'io 10
4/rzr 2 sec.
If the capacity of an air condenser is to be expressed in
farads we have
If the condenser has between its plates a dielectric of which
the inductivity is k, see article 38, then equation (16) becomes
J=kC a -. (18)
* This is precisely the velocity of light. The significance of this fact is explained
in Chapter XV.
36 ELEMENTS OF PHYSICS..
46. Amount of electric flux from an electric charge. Consider
a parallel plate air condenser of capacity J. Substituting the
value of /I = - I from equation (5) in equation (16) we have
Now, is the electric field intensity between the plates (direc-
tion of field perpendicular to the plates) and a is the electric
flux N from plate to plate, according to equation (14). There-
in which C is the constant mentioned in article 45. Therefore
the electric flux outwards from charge Q is proportional to the
charge, and the charge on a body may be expressed in terms of the
number of lines of electric flux which terminate on the body.
47. A new set of electrical units. The factor C in equations
(16), (19) and (20) occurs in many equations relating to electric
charge and electric field. The discussion of electrostatics is
somewhat simplified by so choosing the various electrical units
as to give to C the value In this case equation (20) becomes