If there are three charges arranged along a straight line, then the calculation of the net electrostatic force on any one of the three charges requires you to take into consideration the vector nature of forces.

 

Read

Read the first two paragraphs on page 532 of the textbook then review "Example 10.3."  Be sure to follow the solution carefully, then answer the following Self-Check questions.

 


SC 5.  

Complete "Practice Problems" 1 and 2 on page 532 of your textbook.

 

   Self-Check Answer

SC 5.

  1. The fact that sphere A and sphere C have the same charge means that the distance of separation is the only factor that will produce a difference in the electrostatic forces. In this case, the fact that the force varies inversely with the distance squared provides the key to drawing the free-body diagram. Since sphere C is two times farther away than sphere A, the electrostatic force exerted by sphere C must be ( ) 2  or   as large as the electrostatic force exerted by sphere A.

    This explains why   is four times longer than  .

  2. The net electrostatic force on sphere B is represented by a vector three units long directed to the left. This is the result of the vector addition of  , which is one unit long and directed to the right, combined with   which is four units long and directed to the left.

 

In the previous example and the practice problems, the fact that two of the charges had the same magnitude allowed symmetry to simplify the solution.  The next problems are slightly more complex because this symmetry is not present.

 

Read and Do

Do "Example 10.4" on page 533 of the text.  Be sure to follow the solution carefully.

 

 

Self-Check

Answer the following self-check (SC) question to confirm your understanding of example 10.4.  When ready, click the "Check your work" bar to assess your response.

 

SC 6.  

Complete "Practice Problem" 1 on page 533 of your textbook.

  

   Self-Check Answer

SC 6.

 

Given

 

 

Required

to find the net force acting on sphere 2,

 

Analysis and Solution

Step 1: Determine the direction of the forces.

 

The charge on sphere 1 is negative, and the charge on sphere 2 is positive. Therefore, the electrostatic force of on is an attractive force, pulling to the left. Similar thinking explains why the electrostatic force of on  is an attractive force, pulling to the right.

 

If right is considered to be the positive direction and left the negative direction, then the following free-body diagram illustrates the forces acting on .


 

Note that is longer than  because compared to sphere 3, sphere 1 has a larger charge and is closer to sphere 2.

 

Step 2: Calculate the net electrostatic force on sphere 2.

 

 

Note that the negative sign has been added to communicate that  is directed to the left.

 

 

 

[to the left]

 

Paraphrase

The net electrostatic force on sphere 2 is 1.16 × 10 –4 N, to the left.