Electric Field-Lines

An electric field can be represented diagrammatically as a set of lines with arrows on, called electric field-lines, which fill space. Electric field-lines are drawn according to the following rules:

The direction of the electric field is everywhere tangent to the field-lines, in the sense of the arrows on the lines. The magnitude of the field is proportional to the number of field-lines per unit area passing through a small surface normal to the lines.

Thus, field-lines determine the magnitude, as well as the direction, of the electric field. In particular, the field is strong at points where the field-lines are closely spaced, and weak at points where they are far apart.

Figure 9: The electric field-lines of a positive point charge.

The electric field-lines associated with a positive point charge are a set of unbroken, evenly spaced (in solid angle) straight-lines which radiate from the charge--see Fig. 9. Thus, the tangent to the field-lines is always directed radially away from the charge, giving the correct direction for the electric field. The number of electric field-lines per unit area normal to the lines falls off like $1/r^2$, where $r$ is the radial distance from the charge, since the total number of lines is fixed, whereas the area normal to the lines increases like $r^2$. Thus, the electric field-strength falls off like $1/r^2$, in accordance with Coulomb's law.

By analogy, the electric field-lines associated with a negative point charge are a set of unbroken, evenly spaced (in solid angle) straight lines which converge on the charge.

As a general rule, electric field-lines generated by fixed charges begin on positive charges, end on negative charges, and are unbroken and never cross in the vacuum regions between charges.