Section 3.3 · Home exercises · 4 of 9
Home exercise 3.3.4: Line charge, field on its axis
Line charge, field on its axis
#A line charge of length and uniform density lies on the -axis between and . Find the electrostatic potential and the electric field at a point of the axis with .
Source: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Example 3-10.
Superposition along the line. Because P is on the axis of the line, the distance is simply and the integral is a logarithm. The field on the axis is along by symmetry.
Source and field points both lie on the -axis:
The potential at P is then
By symmetry the field on the axis is along :
Both results have the right units ( in V, divided by a length for ), and both reduce to those of a point charge for (remark below).
For , , so and : from far away the line looks like a point charge . As both diverge, because P reaches the end of the line.