Electric Field Lines

Because an electric field cannot be seen directly, Michael Faraday introduced a simple and enduring way of picturing it: the electric field line, a continuous curve drawn in space such that the tangent to the curve at any point gives the direction of $\vec{E}$ at that point, and the density of such lines (how closely packed they are, i.e. the number of lines crossing a small area held perpendicular to them) represents the magnitude of the field there.

The field-line picture obeys a small set of rules, all of which follow directly from the properties of the electrostatic field:

1. Origin and termination. Field lines always start on a positive charge (or come in from infinity) and always end on a negative charge (or go out to infinity); they are never drawn beginning or ending in empty space with no charge present. For an isolated positive point charge, the lines radiate straight outward in all directions to infinity (Figure 1); for an isolated negative point charge, they converge straight inward from infinity.

2. Field lines never cross. At any single point in space, the electric field has one, and only one, well-defined direction (the vector sum of all contributions at that point). If two field lines were to cross, the field at the crossing point would have to point in two different directions simultaneously, which is impossible -- so field lines can never intersect one another.

3. Line density shows field strength. Where field lines are drawn close together, the field is strong; where they are spread far apart, the field is weak. This is why the lines around a point charge are bunched tightly near the charge (where $E=kq/r^2$ is large) and increasingly spread out farther away (where $E$ falls off).

4. Field lines are continuous curves, never broken. They do not appear or disappear abruptly in the middle of empty space. …