Coefficients of Potential | Coefficients Potential

In electrostatics, the coefficients of potential determine the relationship between the charge and electrostatic potential (electrical potential), which is purely geometric:

$\begin{matrix} \phi_1 = p_{11}Q_1 + \cdots + p_{1n}Q_n \\ \phi_2 = p_{21}Q_1 + \cdots + p_{2n}Q_n \\ \vdots \\ \phi_n = p_{n1}Q_1 + \cdots + p_{nn}Q_n \end{matrix}.$

where Q_i is the surface charge on conductor i. The coefficients of potential are the coefficients p_ij. φ_i should be correctly read as the potential due to charge 1, and hence "" is the p due to charge 2 on charge 1.

or more formally

Note that:

p_ij = p_ji, by symmetry, and
p_ij is not dependent on the charge,

The physical content of the symmetry is as follows:

if a charge Q on conductor j brings conductor i to a potential φ, then the same charge placed on i would bring j to the same potential φ.

In general, the coefficients is used when describing system of conductors, such as in the capacitor.

Read more about Coefficients Of Potential: Theory, Example, Related Coefficients

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