Coefficients of Potential - Example

Example

In this example, we employ the method of coefficients of potential to determine the capacitance on a two-conductor system.

For a two-conductor system, the system of linear equations is

\begin{matrix} \phi_1 = p_{11}Q_1 + p_{12}Q_2 \\ \phi_2 = p_{21}Q_1 + p_{22}Q_2 \end{matrix}.

On a capacitor, the charge on the two conductors is equal and opposite: Q = Q1 = -Q2. Therefore,

\begin{matrix} \phi_1 = (p_{11} - p_{12})Q \\ \phi_2 = (p_{21} - p_{22})Q \end{matrix},

and

Hence,

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