Conceptual Physics

Electric field of multiple charges

Enet = net electric field

Ei= electric field of a charge

23.7 - Drawing field diagrams for multiple charges

Drawing the field diagram of a field generated by multiple charges requires the

application of three rules. To explain them, we use the configuration of two charges

shown in Concept 1. The negative charge is twice as strong as the positive charge.

Rule 1: The number of field lines in a diagram that emanate from a positive charge, or

terminate at a negative charge, is proportional to the magnitude of the charge. In the

diagram to the right, 8 lines emanate from q, and 16 terminate at í 2 q.

Rule 2: Other field lines may start from or extend to infinity. The “other” eight field lines

that terminate at the negative charge, the ones that do not emanate from the positive

charge, start at infinity. In other words, they enter from “outside” the diagram. If the

positive charge were +4q, there would be more field lines emanating from it than

terminating at the negative charge. The “extra” field lines would extend to infinity.

Rule 3: Field lines never cross. A positive test charge located at such an intersection

would be “confused” as to what force it experienced, since the field would point in two

directions. This rule reflects an important point: At any location, a field has a single

direction and magnitude. This point is emphasized in the Concept 2 illustration.

These rules enable you to draw a correct field diagram. They provide a starting point for

drawing a field diagram like the one shown in Concept 1. Considering the nature of the

force experienced by a positive charge at various locations is required to flesh out the

diagram.

A last point to keep in mind: Electric field diagrams are commonly drawn in two

dimensions, but electric fields exist in three dimensions. You usually see field diagrams

on flat surfaces, like a computer monitor, a piece of paper or a blackboard. However,

the field exists above and below the surface of the diagram as well.

Field lines

Incident lines proportional to charge

Start at “+” charges, end at “í” charges

·Excess lines start or end at infinity

Field lines

Do not cross

(^424) Copyright 2007 Kinetic Books Co. Chapter 23