# 3.1 Linear Charge Density Along a Single Conductor

Assuming that a group of n conductors carrying linear charge densities q1, q2, …, qn are located above the ground plane, the voltage of conductor i to ground is

 $V_{i}=\frac{q_{1}ln\left(\frac{D_{i1}}{d_{i1}}\right)+\cdots+q_{i}ln\left(% \frac{D_{ii}}{d_{i}}\right)+\cdots+q_{n}ln\left(\frac{D_{in}}{d_{in}}\right)}{% 2\pi\epsilon}$ (31)

where

qi is the charge of conductor i in coulombs/meter.

di is the radius of conductor i.

Dii is the distance between conductor i and its image (i.e. 2hi in Figure 1).

dij is the distance between conductor i and conductor j.

Dij is the distance between conductor i and the image of conductor j as illustrated in Figure 1.

$\epsilon$ is the permittivity of the medium.

Note: The distances associated with each logarithmic ratio (e.g. di and Dii or din and Din) of Equation 31 must be expressed in the same units.