the charge induced on B; while on A would remain that part of its charge which has its corresponding induced charge on the walls and ceilings, &c., from which we are now insulated. When B is insulated, therefore, we can divide the charge on A into two portions; one part can be withdrawn by a person in connection with the walls, ceiling, &c., and unconnected with B, but cannot be withdrawn by a person connected with B and insulated from the walls, &c.; the other part can be withdrawn by a person connected with B and unconnected with walls, &c., but not by a person insulated from B. The former is free with respect to any person connected with the walls, &c., the latter is bound with respect to such a person.

This is the origin of the terms bound and free; the reader will see in how relative a sense they must be understood.

§ 4. Conditions affecting the Magnitude of the Bound Charge. When B is very close to A we may neglect the 'free' charge on A as relatively insignificant (see § 3). The 'charge' of the condensing system, composed of A and B, will then mean the bound charge' residing on that face of A that is turned toward B; the inseparable accompaniment of an equal and opposite charge on B will be understood, but not generally mentioned.

The magnitude of the charge can be experimentally shown to depend on several conditions.

(i.) On the size of the plates A and B.-If these are equal in area, and if the distance between them be very small as compared with the diameter of either, then the charge will be (approximately) directly proportional to the area of the plates.

(ii.) On the distance between the plates A and B.-The nearer the plates, the greater the charge. And, with the condition just given, the charge is inversely proportional to the distance between the plates.

(iii.) On the difference of potential between the plates A and B.— We have not yet explained exactly in what units we measured electrical level or potential; but we have sufficiently indicated the nature of the unit employed. For further, the reader must wait for Chapter X. §§ 9, 19, 25, &c. We may, however, here state that the charge is directly proportional to the difference of the potentials of A and B.

(iv.) On the nature of the dielectric (see note).-If the charge is

of a certain magnitude Q when the dielectric is air, then cæteris paribus it will be .Q when the dielectric is some other substance. This is (as we shall see in Chapter IX.) the specific inductive capacity of the particular dielectric. If then Q represent the numerical value of the bound charge, V, and V2 the potentials of the plates A and B, and K be a quantity including the area of the plates, the distance between them, and the specific inductive capacity of the dielectric, and called the capacity of the condenser, then we shall have the formula.

when the outer coating is put to earth and so is at zero potential.

Note.-'Dielectric.' Any non-conducting medium, be it solid, liquid, or gas, that intervenes between two conductors, is called a dielectric. It is across dielectrics that electrostatic attractions and repulsions are exerted; and it is in dielectrics that fields of electrostatic force exist. The usual dielectric is air; but in certain instruments glass, or ebonite, is the dielectric.

$5. An Isolated Body considered as the Limiting Case of a Condenser.-If the plate B be at zero potential, then the formula becomes

Q=K.V

where V is the potential of A.

Now, as stated in Chapter V. § 8, it can be shown (see Chapter X. § 19) that when B and all other surrounding bodies are at a distance from A very great as compared with the dimensions of A, then any further change in their positions and distances will make no difference in the capacity of A; that is, under such conditions the value of the capacity K depends only on the size and shape of A.

We thus arrive at our old formula for isolated bodies, viz. :

Q=K. V; or V =

§ 6. Alternate Discharge.-Let us have two equal plates A and B very close together, B being put to earth, and A being charged to its fullest extent; and let us call the charge on A, unity.

The total induced charge answering to the charge + 1 on A
I; and of this the larger part by far will be on B.

will be

--

Let

this larger part be called m, where m is some large proper fraction

; the other being on the walls, &c. Then as long

I 100

as A is untouched we can say that a charge + 1 on A ‘binds' a chargem on B, in the sense that we cannot withdraw it from B as long as A is insulated.

In the same way, since the plates are equal and similarly situated, a charge, I on B would 'bind' a charge + m on A. Or, more generally, a charge Q on either would bind a charge mQ on the other.

In the case we have supposed, the charge + 1 on A binds on B. This charge m on B can bind only + m × m, oi

+ m2, on A.

Hence, if we insulate B and touch A, putting it to earth, we withdraw an amount + (1 − m2) from A, and leave on it + m2

bound by the

The reader may put e.g. m on B.

99 100

for m.

Insulating A and touching B, we withdraw from B what A does not bind; that is, since the + m2 left on A will bind - m3, on B, we leave - m3 on B and withdraw m - m3 from B, and so on.

- m × m2, or

Each time that one plate is put to earth, part of the charge on the other plate becomes 'free.'

This process of alternately putting either plate to earth is called the alternate discharge.

Note.--As regards the exact meaning of m, the reader will understand the following explanation better when he has read Chapter X,

=

Let us consider the plate A only. There is on the inside surface next to B a bound charge Q; and on the outside surface, opposite to the relatively distant walls, a relatively insignificant charge Q'. The charge Q raises the inner surface, and the charge Q' raises the outer surface, to a potential VA, which is necessarily the same for the two surfaces. If then K is the capacity of the inner surface, and K' the capacity of the outer surface, we have the relation VA. We may call K the 'bound capacity' of A, or the capacity of the condensing system, its magnitude depending on the shape and size of A and also on the position &c. of B. We may call K' the 'free capacity' of A— or rather of its outer surface; its magnitude depends on the shape and size of this outer surface, but on nothing else provided that the walls &c. are so remote that the outer surface of A may be considered to be 'isolated' with respect to them. From the relation given above we easily obtain the result that

K

Remembering then that Q + Q' is the total charge on A, and that the charge on B equals Q in magnitude, we see that m=

K
K+K'

Experiments.-(i.) With the plates A and B, each connected with a Peltier electrometer, the alternate discharge can be shown; though the arrangement is not one adapted to give indication for more than a few discharges. As we touch A we receive a spark, and ЕB, previously undeflected because at zero potential, will be deflected with electricity, B and EB being now at a potential, while EA will fall to zero deflection. If we now touch В, Е falls to zero and EA is deflected with +, and so on.

(ii.) A Leyden jar (see next section) is mounted on an insulating stand. While it is being charged the outer coating is put to earth, and then the whole is left insulated.

We can, by alternately touching the knob connected with the inside, and the outside coating, draw off sparks of + and electricity in turns. The

signs of these alternate charges can readily be tested as in Chapter IV.

§ 7. Leyden Jars.—When it is required merely to store a large charge at the potential of the source, and when there is no need to alter the distance between the plates, the condenser usually takes the form of a jar of glass having inside and outside coatings of tin-foil. A knob gives connection with the inside of the jar; this knob should, if possible, pass up from the inside without any connection with the neck of the jar, in order to insure good insulation.

Since the charge, cæteris paribus, is proportional to the differ

ence of potential of outside and inside, it should be our object to make this difference as large as possible. As a rule the highest available potential is that of our source, and with this we connect the knob; the lowest available is the zero potential of the earth, and so we put the outside coating to earth.

A larger charge would be obtained if we could put the outside to a potential.

When the outer coating is to earth, the charge of the jar is determined by the formula Q=K.V

where K is the capacity of the jar, and V is the potential of the inner coating.

It is

Glass is used for several reasons. easy to make glass jars; glass has a high specific inductive capacity (see Chapter IX.); and the jar can be made thin, or the distance between the plates small and therefore the capacity of the jar large, without a discharge taking place through the glass.

For the calculation of K, as well as for the units in which V is measured, the reader is referred to Chapter X.

§ 8. The Unit Jar.-If we can fix the capacity of a jar and the difference of potential between its two coatings, then we have fixed the charge in that jar.

A unit jar is a small Leyden jar of some convenient shape; usually so made as to admit of easy cleaning and drying, and to insulate well.

Connected with the outside is a knob B, and connected with the inside is a knob A, whose distance from B can be regulated by sliding the piece AC along the graduated rod DE.

It is proved experimentally that the distance between A

and B across which the jar will just discharge itself is directly proportional to the difference of potential between A and B.