Chapter 2: E-field and the Principle of Superposition

Interactive 2

The electric field intensity vector E is the force that would act on a unit test charge if this charge is inserted in the volume where the electrostatic field exists, . It is a normalized measure of the strength of the field and its direction.

In a linear medium, the principle of superposition holds. According to it, the electric field at an observation point is the vectorial sum of the individual contributions (fields) of all present charges in the region of interest, .

In the set-up below, we have two point charges (red and blue points), whose individual E-field vectors at the observation point P are given by

where  is the i-th charge value,  is the distance from the i-th charge to P, and  is the unit vector pointing from the i-th charge toward P.

The values of the charges are fixed. You can, however, change the sign of the second charge . Click on the observation point (black point), and drag to any location within the shaded area. Observe the strength and direction of the overall field vector E (the black arrow). To appreciate better the vectorial nature of this superposition, the individual field vectors,  and  (red and blue arrows, respectively), are also plotted.

Since this is a 2-D planar illustration, the motion of the observation point is limited to a plane. These interactive plots, however, fully represent reality, since the three charges—the two sources and the test-charge—always define a plane (unless they are perfectly aligned in a line), which contains all three field vectors.

 
Interactive Applet

E-field and the Principle of Superposition