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B, respectively, and therefore this force is proportional to some
function of the difference of potential between A and B. If
A or B be very small, they would part with a considerable portion
of their charge when connected to C and D and the resultant
potential would be less than the original potential, but usually
A and B are so large that the small loss of potential can be neg-
lected. For example, B is frequently the earth, in which case D
is of zero potential.

Coulomb's torsion balance, already described, may be used as
an electrometer, the removable ball being touched to the body
whose potential is required and thus obtaining a charge propor-
tional to that potential, but the usual form of electrometers use
plates or flat moving parts instead of the spheres described above.

101. The Attracted Disc Electrometer. The attracted disc
electrometer was invented by Snow Harris but perfected by Lord
Kelvin. Its essential parts are shown diagrammatically in Fig. 44.
AB is a lever pivoted upon a tightly stretched horizontal wire CD.
At one end is a counterpoise B, at the other end a fork A which
embraces an upright E and across which there is stretched a fine
hair. From the fork there is suspended so as to hang horizontally
a circular disc G which moves with a minimum clearance inside of
a fixed ring R. A portion of this ring is represented in the diagram
as cut away. Below the disc and ring is a circular plate P insu-
lated by being mounted upon a glass stem which in turn is attached
to a brass support. The plate P can be raised or lowered by turn-
ing the micrometer screw H, which is so arranged that the plate



STATIC ELECTRICITY. 79

is always kept strictly parallel to the disc G and which permits the
distance through which P has been moved to be read with great
accuracy. Upon the upright E there are two black dots and when
the lower surface of G is exactly in the plane of the lower surface




Fig. 44.

of R the hair at A is just between these dots. There is a lens L
by which the position of the hair is observed and it is said that an
error of as little as 1/50,000 of an inch can be detected and cor-
rected. G and R are connected electrically by means of a wire from
R to D. By moving the counterpoise B or by twisting the wire
CD, the disc G is given an initial position slightly above the ring
R. Small weights are then placed upon G until the lower surfaces
of G and R lie in a common plane. From the weights used the
force in dynes to effect this is determined. The weights are then
removed. If now a charge be given to G it will induce an opposite
charge in P, G and P will attract each other and G will be drawn
downward. By varying the position of P the downward pull on
G can be so adjusted that the plane of the lower surface of G coin-
cides with that of the lower surface of R. At this point, the force
of attraction equals the force in dynes as determined by the weights.

102. Theory of Attracted Disc Electrometer. In Par. 40 we

saw that a charge imparted to a flat disc was uniformly distributed
over the central portion but much denser around the edges. When
G and R are in one plane they practically constitute one surface.
The surface density over the movable disc G is therefore quite
uniform and the excessive density is confined to the fixed ring R
which on this account was called by Lord Kelvin the "guard ring."



80 ELEMENTS OF ELECTRICITY.

To measure the difference in potential between two bodies, R
(and hence G) is connected to one and P to the other. Let V be
the potential of P and V" that of G. The surface density of G
is 6 and that of the induced charge upon P is - 5. The difference
of potential, V'-V", is measured (Par. 72) by the amount of
work done in moving a unit positive charge from P to G, a dis-
tance D. The force exerted upon a unit charge placed between
P and G is (Par. 66) an attraction of 2 wd by one and a repulsion
of 2 7J-5 by the other, or a total force of 4 nd. The work therefore is

V'-V" =47r5D

Again, every unit charge upon G is attracted by P with a force
of 2 7r6 dynes. If S be the area of G,' the charge upon G is Sd and
the total force of attraction is

F = 2wd z S

Whence / p

8



Substituting in the expression for V V", we have

V- V" = D\/^jr-

F is determined in dynes from the weights as described above,
D is in centimeters, S is in square centimeters and V V", the
difference in potential, is in absolute electrostatic units. As
explained in Par. 77, if this be multiplied by 300 it is converted
into volts.

Since S is constant and F may be kept constant, the expression

SirF

is a constant and can be determined once for all. The

difference of potential between G and P is therefore directly pro-
portional to the distance between the plates when the instrument
is balanced.

The actual distance between the plates is difficult of measure-
ment. If P be connected to some other charged body whose
potential is V" and the apparatus be balanced we have

V"- v = iXV^fr

* o

Subtracting this from the expression above we have



STATIC ELECTRICITY.



81



that is, the difference of potential between two charged bodies,
each being compared to a third, is proportional to the difference
in the distance between the plates in the two observations and
this difference in distance is easily and accurately determined from
the micrometer screw.

By using the earth as the third body, that is, by connecting G
to the earth, V" in the above becomes zero.

There are many refinements used in connection with this instru-
ment but it is not necessary to describe them here.

103. The Quadrant Electrometer. The quadrant electrom-
eter of Lord Kelvin is a more sensitive instrument than the




Fig. 45.

foregoing. It is shown diagrammatically in Fig. 45. A flat
cylindrical brass box is cut into quadrants A, B, C and D (this
last is represented as cut away to show the interior) which are
fastened to the top of the apparatus (not shown) by the glass
pillars E, F, etc. The diametrically opposite quadrants A-C and



82 ELEMENTS OF ELECTRICITY.

B-D are connected by wires (Fig. 46). Within the box is a flat
needle N of light aluminum plate which is fastened rigidly to an
aluminum wire extending above and below. The needle is sus-
pended by one or by two fibres of silk or by a single fibre of quartz
L attached to the upper end of this wire. To the lower end of the
wire there is fastened a platinum wire which dips into some sul-
phuric acid in a glass jar: This jar, which also serves as a case for
the lower part of the instrument, has an outer coating of tin-foil
and with the sulphuric acid within is thus a Leyden jar. The
acid also keeps the air in the jar dry and prevents loss of charge by
moisture. The needle swings midway between the top and bottom
of the box and symmetrically over the separation between the
quadrants. Upon the wire above the needle there is fastened a
small circular concave mirror M. The angle through which the
needle turns is determined either by the reflection of a beam of
light from this mirror upon a scale or by observing in the mirror
by means of a telescope the reflection of a printed scale fastened
just above the telescope. These methods of determining the angle
of deflection are described in detail later on; the former in connec-
tion with the mirror galvanometer (Par. 377), the latter in con-
nection with the suspended coil galvanometer (Par. 378). There
project from the glass case terminals, called "electrodes," one of
which connects with each pair of quadrants and one with the acid
of the jar.

To use the instrument, one pair of quadrants is connected to
one body, the other pair to the second body between which the
difference of potential is to be measured. The quadrants thus
acquire the potentials of the respective bodies.
The Leyden jar is then charged until the needle
has a high potential V 3 which by certain arrange-
ments, not necessary to describe here, is kept
constant during the measurement. If the
charges are of the same kind, mutual repulsion
Fi 46 exists between the charge on the needle and

those on the adjacent quadrants and the needle
moves toward the quadrant of lesser charge, that is, of lower po-
tential. The deflection of the needle is read from the mirror and
the difference of potential is proportional to this deflection.

This instrument is sufficiently delicate to measure differences
of potential almost as small as .01 of a volt.





STATIC ELECTRICITY. 83

104. Theory of the Quadrant Electrometer. Figure 47 repre-
sents a cross-section of the needle and two adjacent quadrants,
the potentials being as marked and y 3 being much greater than
either of the others. V\ Y 3
constitute a condenser, V 2 V 3
another. The energy of a con-
denser (Par. 97) is %V 2 K in
which V is the difference in
potential between the two Fi s- 47>

plates and K is its capacity. The energy of Vi V 3 is thereiore

and that of y 2 V s is

y 3 being symmetrically suspended with respect to V\ and V 2 as
it swings to the right or left it increases the surface embraced by
one by exactly the same amount as it decreases the surface em-
braced by the other and as its edges still remain well inside of
Vi and y 2 it increases the capacity of one condenser and decreases
by an equal amount that of the other. Let this increment of
capacity for a unit angular motion of Y 3 be denoted by k; the
decrement will be A:. The change in the energy of Vi V 3 for an
angular movement 6 will therefore be JA0(V 3 Vi) 2 and that
of V 2 V 3 will be - %ke (Y 3 -V 2 ) 2 . The total change in the
energy of the system will be




The force moving the needle = = i s therefore

pat



F=

or the force between the needle and each quadrant is proportional
to the square of the difference of potential between the needle and
the respective quadrant.

Simplifying the foregoing expression we have



or the force tending to turn the needle is proportional to the
difference of potential between the quadrants and also to the
difference between the potential of the needle and the average of
the potentials of the two quadrants.



84 ELEMENTS OF ELECTRICITY.

Since V 3 is kept constant and is very large as compared to Vi
and V 2 , [ Vi - * 1" ? J may be taken as a constant and the ex-
pression for the force becomes

F = a (Vi-V 2 )

The force being counterbalanced by the torsion of the sus-
pending fibre, the difference of potential, Vi V 2 , between the
two bodies being examined is proportional to the deflection as
indicated by the mirror. By using a known difference of potential
the constant a may be determined once for all.



MAGNETISM. 85



PART II.
MAGNETISM.



CHAPTER 12.

MAGNETS.

105. Natural Magnets. Of the four important ores of iron the
richest is that one whose chemical formula is Fe 3 4 . This when
pure is a heavy black mineral, often coarsely crystalline but also
frequently massive. It occurs in beds in many widely scattered
localities and from it a large part of the iron and steel of commerce
is made. Some specimens of this ore possess the remarkable
property of attracting and picking up small particles of iron and
steel. If such a specimen be dipped or rolled in iron filings, the
filings will adhere to it like a mossy growth. This property has
been known for nearly 3,000 years and because the best speci-
mens came from the vicinity of the town of Magnesia in Lydia
they were called by the Greeks magnetis lithos (Magnesian or
Magnetian stone), whence are derived our name magnet and the
mineralogical term magnetite or magnetic iron ore. To distinguish
these magnets from those prepared artificially they are usually
called native or natural magnets.

106. Lodestones. About 800 years ago an additional property
of magnets, equally as remarkable as the first, became known to
European nations. If an oblong or elongated magnet be arranged
so that it is free to rotate in a horizontal plane (as for example by
suspending it by a thread or by placing it upon a floating cork or
by balancing it upon a pivot) it will take up a north and south
position, the same end always returning to the north, no matter
what may be its primary position. This property was quickly
utilized in navigation and since these magnets thus led the
mariner about over the seas, they were called lodestones (leading
stones).



86 ELEMENTS OF ELECTRICITY.

107. Fables of the Ancients. In contemplating the mystical
power of attraction of magnets, the ancients gave free rein to their
imagination and gravely recorded and copied from each other's
writings the most wonderful statements about magnets. They
were by some reputed to be endowed with life and to possess a
soul. A magnet was supposed to protect from witchcraft. If
held in the hand it cured cramps. The power of a weakening
magnet could be restored by soaking it in the blood of a buck
while if it were rubbed with garlic it lost its power. It also lost
its power when in the presence of a diamond. If pickled in salt
with a certain fish, the remora or sucking fish, it acquired the
property of attracting gold and silver and could thus be used to
fish up treasure from the deepest wells. At various points in the
Eastern Seas were islands of lodestone so powerful that they pulled
the nails from the sides of vessels and thus caused their loss. In
those parts ships had to be built with wooden pegs. In India
there were side by side two mountains, one of lodestone so power-
ful that if a person with iron nails in his shoes stepped upon it he
could not raise his feet to take a second step, the other of a sub-
stance which repelled iron so strongly that such a person found it
impossible to place his foot upon the surface. We can not now
understand the state of mind of these writers, for very simple
experiments would have readily shown the absurdity of their
statements.

108. Doctor Gilbert. Such for near 2,000 years remained the
state of knowledge until, as has already been stated (Par. 12), a
certain Doctor Gilbert in the reign of Queen Elizabeth undertook
a series of investigations of the properties of the lodestone. In
1600 he published his work, De Magnete Magneticisque Corporibus
(On the Magnet and Magnetic Bodies), in which he described his
experiments, wonderful for their simplicity and in some directions
well nigh exhaustive. Anticipating the Baconian system, he
accepted no statements about magnets until he had confirmed
these statements by his own experiments and he was thus able
not only to sweep aside the mythological rubbish which until then
passed current but also to bring forward many facts, hitherto
unknown. In short, by his researches he brought to light the
majority of the truths and principles upon which our present
knowledge of magnetism is based.






MAGNETISM.



87




109. Artificial Magnets. If a bar of iron or of steel be rubbed
or stroked in a certain manner (see Par. 162) by a lodestone, the
bar acquires magnetic properties. Steel is found to be more reten-
tive of magnetism than iron and is accordingly used. The bar
thus magnetized may in turn be used to produce magnetism in
others. There is another and better method, in which an electric
current is used to produce magnets, but an explanation of this
method must be deferred until later (Par. 164). These artificial
magnets, on account of their strength, of the ease with which they
may be prepared and of the

readiness with which they may
be given any desired shape,
have quite displaced lodestones
and are the ones referred to in
the following pages. The com-
monest forms are bars and the

so-called needles. These last ^^^^ Fig. 48.

are usually thin, elongated, losenge-shaped magnets with a socket
at the center by which they may be pivoted upon a sharp point
(Fig. 48). In the best needles the socket is jewelled.

110. Magnetic Poles. In pursuing a certain line of investi-
gation, Gilbert caused to be cut from a lodestone a regular sphere
to which he applied the name terrella (little globe). When this
terrella was rolled in iron filings they adhered to it in tufts, not
however uniformly over its surface but upon two restricted areas
at the opposite ends of a diameter. These regions he designated
as the poles of the terrella.

If a bar magnet or a magnetic needle be dipped in filings, they
will adhere only to the regions at the ends, and these regions are

likewise called poles.

If such a magnet be balanced
upon a cork which in turn floats
in a vessel of water (Fig. 49)
it will oscillate in a horizontal
plane and finally come to rest
in a north and south position.
The same end of the magnet

Fig. 49. always points north and is

therefore called the north pole, the other end being called the
south pole. The fact that this one end always points north shows




88 ELEMENTS OF ELECTRICITY.

that it must differ from the other, but so far as the attraction
of iron filings and the lifting of iron weights is concerned, the two
ends are of identical properties. The north and the south poles
are frequently designated positive and negative, respectively.

111. The Poles Inseparable. Should a slender bar magnet
(Fig. 50) be broken in half, it will be found that each half is a
complete magnet and has a north and a south pole nearly as

s N



N



Fig. 50.

strong as those of the original magnet. If one of these halves be
again broken, the fragments will each have a north and a south
pole and so on. In other words, it is impossible to get a separate
north or south pole unaccompanied by an equal pole of the oppo-
site kind. Explanation of this fact will be given later (Par. 152).

112. Magnetic Attraction. If a bar magnet be dipped into
iron or steel filings and then be lifted, the filings will be found to




Fig. 51.



cling to it like a thick mossy growth (Fig. 51). Upon examination
the following peculiarities will be noted.

1st. As already stated, the filings do not adhere all over but
mainly in the region of the poles and none at all in the central
portion of the magnet.

2nd. The individual filings cling to the magnet by their ends
rather than by their sides and at each pole radiate from an internal
focus near the end of the magnet.

3rd. The filings cluster more thickly along the edges and corners
of the magnet than along the flat surfaces.



MAGNETISM.



89



4th. Where the filings are thickest, it will be found that those
which cling to the magnet may have others clinging to them in
turn, and these may have still others, forming, as it were, chains.

113. The Attraction Takes Place Through Intervening Bodies.

The magnetic attraction takes place at a distance and through
space, although it falls off rapidly as the distance increases. Fine
filings will leap up to reach a strong magnet held above them.
Furthermore, the attraction is propagated through intervening
objects. A bar magnet inserted in a glass tube will attract filings
through the glass. If filings be sprinkled upon a thin board or a
slate or a sheet of glass or of brass, a magnet moved about beneath
will drag after it the filings on top. There is but one screen for
the magnetic force and that, as will be explained later (Par. 143),
is a comparatively thick plate of iron or steel.

114. The Attraction Mutual. If a small iron bar be floated
upon a cork in a basin of water, the bar and cork will move about
in pursuit of a magnet held near. If the bar and the magnet be
made to change places, the magnet will follow about after the iron
bar.

115. Action of Magnets upon Each Other. The mutual action
of magnets is most easily studied by means of a magnetic needle.
If when the needle has come to rest, its north end be approached




Fig. 52.

by the north end of a bar magnet (Fig. 52), it will be repelled and
move off. On the other hand, its south end will be attracted by
the north end of the magnet. If the bar magnet be turned end
for end and its south end be held to the north end of the needle,
the latter will be attracted, and if it be held to the south end, this
end will be repelled. We see then that magnetic poles follow a law



90



ELEMENTS OF ELECTRICITY.



similar to that given for positive and negative charges of elec-
tricity (Par. 24), that is, like poles repel and unlike poles attract
each other.

If two bars of similar shape and size attract each other we
would know that one of them was a magnet but without other
test could not tell which. If they repelled each other we would
know that they were both magnets.

116. Why a Magnetic Needle Points North and South. Sup-
pose that upon a bar magnet resting on a horizontal surface there

be placed, as shown in Fig.
53, a magnetic needle. The
north pole of the magnet
will repel the north pole of
the needle but will attract
its south pole; the south pole




Fig. 53.



of the magnet will repel the



south pole of the needle and attract its north pole. The needle
will in consequence take up a position parallel to the axis of the
bar magnet but with its poles in reverse direction. Similar experi-
ments led Gilbert to the discovery that the earth itself is an immense
magnet, its poles being in the neighborhood of, but not coinciding
exactly with, the geographical poles. A magnetic needle will
therefore take up a position approximately in the plane of the
earth's magnetic axis for the same reason that the needle in
the above experiment poised parallel to the axis of the bar
magnet.

117. The Poles Misnamed. Gilbert called attention to a fact
following directly from his discovery, that is, that the pole of the
needle which is attracted by the earth's north magnetic pole (and
which we have called its north pole) should strictly be called its
south pole. Subsequent writers in view of this have sought to
avoid confusion by using the terms "north-seeking pole" and
"south-seeking pole," but it is thought that the shorter expres-
sions are sufficiently sanctioned by custom and that no ambiguity
will arise if in the following pages the pole of the needle which
points north be designated its north pole, the other, its south
pole.

118. Magnetization by Induction. A soft iron nail touched
to a bar magnet will cling to it. If a second nail be now touched,






MAGNETISM.



91




not to the magnet but to the first nail (Fig. 54), it will cling to this
nail and even a third nail may be attached to the second and so on.
If while thus dangling the several
nails be tested, each will be found
to possess polarity, the upper ends
being of opposite polarity to that
end of the magnet to which they
are clinging, the lower ends being
of the same polarity. If the mag-
net be removed the chain of nails
will fall apart. The magnet there- Fi g- 54 -

fore influences the nails so that for the time being they them-
selves are magnets. This is the explanation of the chains of filings
referred to in Par. 112. The phenomenon is called magnetization
by induction.

119. Induction Takes Place Through Space. Actual contact
is not necessary for induction. A piece of iron or steel placed
anywhere in the vicinity of a magnet becomes temporarily a
magnet. This fact is clearly shown by the following experiment.
A soft iron bar AB (Fig. 55) free from magnetism is arranged




Fig. 55.

upon a convenient support. Near the end B but not so near as
to be attracted into contact is placed a needle. If the north
pole N of a bar magnet be approached to the end A of the iron
bar, but not actually touching the same, the north pole of the
needle will be repelled from B. The bar A B becomes a magnet
by induction, the end B becoming the north pole and repelling
the north pole of the needle. To show that the repulsion of the
needle is not due to the direct action of the bar magnet, if A B be
removed the effect of the bar magnet upon the needle is almost
negligible.



92 ELEMENTS OF ELECTRICITY.

120. Magnetic Attraction Explained. The foregoing enables
us to explain magnetic attraction. A piece of iron or steel near a
magnet becomes a magnet by induction. The near end of the
piece is of opposite polarity and hence attracted; the farther end
is repelled but the attraction is stronger than the repulsion (mag-
netic attraction and repulsion will shortly be shown to follow the
law of inverse squares) and the piece, if free to do so, will move
bodily up to the magnet. As in the case of electric charges, in-
duction precedes attraction.

121. Other Magnetic Substances. We have heretofore men-
tioned only iron, steel and the lodestone as being magnetic sub-
stances. Two other metals, nickel and cobalt, are noticeably
magnetic, though much less so than the above mentioned, and many



Online LibraryWirt RobinsonThe elements of electricity → online text (page 8 of 46)