Page:Encyclopædia Britannica, Ninth Edition, v. 8.djvu/44

Rh ELECTRIC! T Y [ELECTEOSTATICAL THEORY. Parallel of them raised to potentialV, while the other is connected plates, with the earth, then there will be certain charges E and F on the two plates. If p and r be the coefficients of self- induction for A and B, and q the coefficient of mutual induc tion, then in the present case E-pV, F = ?V, and the energy of the distribution is obviously mula tors. so that the work done by completely discharging the con denser ocV 2. If we suppose the plates very large com pared with the distance between them, then we may treat the case, for all points not very near the edge, as if the plates were infinite. In this case the lines of force are straight, anil the number of lines of force which leave any area on A is equal to that of those which enter the opposite area on H. Hence the surface densities on the plates are equal and opposite in sign. Also we clearly have 1 V f A I  ^^M ...... (44) &quot; For l.he number of lines of force which cross any unit of area parallel to the plates is constant, and therefore the resultant force is con stant at every point between the plates. Principle It appears, therefore, from (44) that if we make the dis- of accu- tance between our plates very small, the density on the inner surface will be very great, and the whole charge on A very great. An apparatus of this kind for collecting large quantities of electricity at a moderate potential is called an accumulator or condenser. One of the first instru ments of this kind was Franklin s pane, which consisted of two sheets of tinfoil pasted opposite each other on the two sides of a pane of glass. There is of course a practical limit to the increase of capacity in such arrangements, because a spark will pass when the insulating medium is too thin. The greater dielectric strength of glass makes it more convenient than air for an insulating medium, and we shall see by-and-by that it has other advantages as well. When the plate A is of finite size there will in general be a distribution of electricity on the back comparable with the charge which A would hold at potential V if B were absent. When the distance between the plates is small, by far the greater portion of the capacity is due to the Condens- presence of B. Advantage of this principle has been taken in the condensing electroscope of Volta, which is an ordin ary gold-leaf apparatus, except that the knob is replaced by a circular disc on which is placed another disc fitted with an insulating handle ; the discs are covered with a thin coat of varnish which serves as an insulating medium. If we connect with either disc, say the lower, a source of electricity of feeble potential V, and connect the upper disc at the same time with the earth, then a large quantity of electricity at potential V collects on the lower disc. Now remove all connections, and lift away the upper disc. The capacity of the lower disc is thereby enormously di minished. Therefore, since the charge is unaltered, its potential must rise correspondingly ; and the gold leaves may diverge very vigorously, although a simple connection with the lower disc alone would scarcely have moved them. This instrument is of great use in all cases where we have an unlimited supply of electricity at feeble potential. Sir William Thomson has devised an accumulator of measur able capacity, called the Guard Ring Accumulator, which is a modification of the arrangement we are discussing. AB (fig. 14) is a flat cylindrical metal box, the upper end of which is truly plane, and has a circular aperture, into which fits, without touching, a plane disc C, which is supported on the bottom of the box by in sulating supports, so that its upper surface is in the same plane with the lid of the box. DE is a metal disc which can 14 be moved by a screw through measured distances, always remaining electro scope. Onard ring ficcumu lator. parallel to AB. When desired, C can be put in communication with AB. It may then be regarded as forming part of an infinite plate, so that if AB be at potential V, and DE at potential zero, then the surface density on C will be equal to^r -,, where d is the distance between the plates ; and if A be the arna of C the whole AV amount of electricity on C is j-j. If now we break the connec tion between C and the box and discharge the box, we are left with AV a known quantity of electricity on C, viz. -r, The most usual and for many purposes the most con- Ley&amp;lt;] venient form of accumulator is the Ley den jar. This isJ ar - merely a glass jar (fig. 15) coated to a certain height out side and inside with tinfoil. The mouth of the jar is stopped with a cork or wooden disc, which serves the double pur pose of keeping dirt and moisture from the uncovered glass inside, and of carrying a wire in metallic connection with the inside coating, which passes up through the stopper and ends in a metal knob. If the glass of the jar be very thin, we may find the distribution on the two coatings by neglecting the curvature ; the electric density on the inner surface of the two coatings will then be the same as in the case of parallel plates. If, therefore, the inner coat ing be at potential V, and the outer at potential zero, the density on the inner coating will be --, &amp;gt; and that on 4ird the outer - -. In the particular case we are consider ing the inner coating forms very nearly a closed conductor, so that there will be very little electricity on its inner sur face, and there will also be very little on the wire and knob compared with the amount on the surface of the inner coating which is next the glass. We may therefore put SV for the whole electricity on the inner coating -j,-, where S is the extent of its surface. The capacity C of the jar is then given by C-JL (45). Green calculated to a first approximation the effect of the curva ture on the capacity, and found that, if K and R be the greatest and least radii of curvature of the inner coating at any point, then the densities on the inner and outer coatings are given by (46), and consequently the capacity of the inner coating by In any case, C being a constant, we have charge E = CV Batte and energy Q = ^CV 2. Hence if we connect the inner of J ai coatings of n similar jars, and charge them to potential V, abrea all the outer coatings being at the same time connected with the earth, we have, E and Q representing the whole charge and energy, E-CV Q--S (48). If we discharge such a battery of n jars into another of n similar jars, by connecting the knobs together, and the outer coatings to earth in each case, we have, U being the common potential after discharge, There is therefore a loss of energy represented by that is 77CV S (49). (50).