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Illustration 23.3: Field-Line Representation of Vector Fields
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There are different ways to represent the electric field created by a charge distribution. One way is to use field vectors (as you've already seen), but you may find it a bit tedious (and difficult unless you carry around a colored pencil set) to draw that on your paper. Many books use electric field lines as an alternate representation of field vectors.
Switch between the field-vector and the field-line representation for Configuration A. What is the difference between the two representations? In a field-line drawing, the line density is often used to represent, at least qualitatively, field strength (more field lines in an area indicate a larger electric field). The arrows represent the direction of the electric field. Now move the charges around in Configuration A. How does the field-line representation reflect the change? Pick a point on a field line. Switch to the vector field representation. What does the field vector look like at that point? Notice that the field vector points in a direction tangent to the field line at any point.
Now, consider Configuration B and look at the two representations. Can you tell if the net charge distribution is positive, negative, or zero? Move the charges to check your answer (you can put them all on top of each other).
Illustration authored by Anne J. Cox and Melissa Dancy.