• Electric Field due to a Multiple Charge Distribution

Topics:  Electric field, Coulomb's law, charge distribution, vector addition, vector algebra.

Pre-requisite skills: Qualitative summation of vectors, Coulomb's law.

Approximate completion time:  Under an hour.

Provide sufficient detail to verify that the assignment was completed in a meaningful manner.

Applet by Physics 1

1.  In the figure below is a layout of three charges.  Each charge  has the same value (although obviously not the same sign) and is separated by a distance a from the other.   There are also two points shown in the figure, point A and point B.  Each point is also a distance a from the nearest charge.

(Note: In the following questions you may find it convenient to set the value of each charge Q = 1 mC or Q = -1 mC.   Assume the distance a is measured in meters.)

(a)  In which direction will the net electric field point at points A and B?

(b)  Using Coulomb's law, determine whether point A or point B will correspond to a stronger electric field.  (You should not have to substitute a numerical value for the distance a in order to answer this question.)

(c)  Using the above applet, place the charges in the applet window in order to mimic the charge distribution in Fig. 1.   Does the resultant electric field shown in the applet confirm your results?  (Hint:  How is the strength of an electric field represented by the plot in the applet?)

2. In terms of comparing the electric field at points A and B, does it matter whether you use the correct value of the Coulomb constant k?

3.   Suppose we had made the value of each charge four times larger than that specified above.  Would that affect the comparison between the electric field at points A and B?

4. How would your results change if the negative charge was placed in the middle and the two positive charges were placed on the outside?  Explain in terms of symmetry.