Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/424

From Wikisource
Jump to: navigation, search
This page has been proofread, but needs to be validated.
382
[331.
CONDUCTION IN DIELECTRICS.

ance R, and let a current be passed along this series from left to right.

Let us first suppose the plates B_0,\, B_1,\, B_2, each insulated and free from charge. Then the total quantity of electricity on each of the plates B must remain zero, and since the electricity on the plates A is in each case equal and opposite to that of the opposed

Fig. 25.

surface they will not be electrified, and no alteration of the current will be observed.

But let the plates B be all connected together, or let each be connected with the earth. Then, since the potential of A_1 is positive, while that of the plates B is zero, A_1 will be positively electrified and B_1 negatively.

If P_1,\, P_2, &c. are the potentials of the plates A_1,\, A_2, &c., and C the capacity of each, and if we suppose that a quantity of electricity equal to Q_0 passes through the wire on the left, Q_l through the connexion R_1, and so on, then the quantity which exists on the plate A_1 is Q_0-Q_1, and we have


 Q_0-Q_1 = C_1P_1.
Similarly Q_1-Q_2=C_2P_2,

and so on.

But by Ohm's Law we have


\begin{align}P_1-P_2 &=R_1 \frac{{dQ_1}}{{dt}}, \\ P_2-P_3 &=R_2 \frac{{dQ_2}}{{dt}}. \end{align}


If we suppose the values of C the same for each plate, and those of R the same for each wire, we shall have a series of equations of the form