5.6 Electric field lines  (Page 2/5)

There is a more useful way to present the same information. Rather than drawing a large number of increasingly smaller vector arrows, we instead connect all of them together, forming continuous lines and curves, as shown in [link] .

Although it may not be obvious at first glance, these field diagrams convey the same information about the electric field as do the vector diagrams. First, the direction of the field at every point is simply the direction of the field vector at that same point. In other words, at any point in space, the field vector at each point is tangent to the field line at that same point. The arrowhead placed on a field line indicates its direction.

As for the magnitude of the field, that is indicated by the field line density    —that is, the number of field lines per unit area passing through a small cross-sectional area perpendicular to the electric field. This field line density is drawn to be proportional to the magnitude of the field at that cross-section. As a result, if the field lines are close together (that is, the field line density is greater), this indicates that the magnitude of the field is large at that point. If the field lines are far apart at the cross-section, this indicates the magnitude of the field is small. [link] shows the idea.

In [link] , the same number of field lines passes through both surfaces ( S and $S\text{′}),$ but the surface S is larger than surface $S\text{′}$ . Therefore, the density of field lines (number of lines per unit area) is larger at the location of $S\text{′}$ , indicating that the electric field is stronger at the location of $S\text{′}$ than at S . The rules for creating an electric field diagram are as follows.