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A vector plot of the electric field due to two sources. The sources are not shown. The field is represented by arrows in an x y graph. Both x and y are in meters and both scales are from -2 meters to 4 meters. Near the origin, the arrows are long and point away from it. Near the point at coordinates 2, 0 the arrows are long and point toward the point. The arrows get smaller as we move farther from those two location and point in intermediate directions.
The vector field of a dipole. Even with just two identical charges, the vector field diagram becomes difficult to understand.

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] .

In part a, electric field lines emanating from a positive charge are shown as straight arrows radiating out from the charge in all directions. In part b, a pair of charges is shown, with one positive and the other negative. The field lines are represented by curved arrows. The arrows start from the positive charge, radiating outward but curving to end at the negative charge. The outer field lines extend beyond the drawing region, but follow the same behavior as those that are within the drawing area.
(a) The electric field line diagram of a positive point charge. (b) The field line diagram of a dipole. In both diagrams, the magnitude of the field is indicated by the field line density. The field vectors (not shown here) are everywhere tangent to the field lines.

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.

Seven electric field lines are shown, generally going from bottom left to top right. The field lines get closer together toward the top. Two square areas, perpendicular to the field lines, are shaded. All of the field lines pass through each shaded area. The area toward the top is smaller than the area toward the bottom.
Electric field lines passing through imaginary areas. Since the number of lines passing through each area is the same, but the areas themselves are different, the field line density is different. This indicates different magnitudes of the electric field at these points.

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

Problem-solving strategy: drawing electric field lines

  1. Electric field lines either originate on positive charges or come in from infinity, and either terminate on negative charges or extend out to infinity.
  2. The number of field lines originating or terminating at a charge is proportional to the magnitude of that charge. A charge of 2 q will have twice as many lines as a charge of q .
  3. At every point in space, the field vector at that point is tangent to the field line at that same point.
  4. The field line density at any point in space is proportional to (and therefore is representative of) the magnitude of the field at that point in space.
  5. Field lines can never cross. Since a field line represents the direction of the field at a given point, if two field lines crossed at some point, that would imply that the electric field was pointing in two different directions at a single point. This in turn would suggest that the (net) force on a test charge placed at that point would point in two different directions. Since this is obviously impossible, it follows that field lines must never cross.
Practice Key Terms 2

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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