#### An Example in One Dimension

Three charges of equal magnitude are equally spaced along a line. The charge on the left is negative, and the other two charges are positive.

If we take the negative charge away, the charge on the right experiences a force of 4F. If we now return the negative charge to its original position and remove the positive charge in the center, what is the magnitude of the force experienced by the charge on the right?

1. F
2. 2F
3. 4F
4. None of the above.

The distance between the charges is larger by a factor of 2. The force goes as 1/r2, so the force is reduced by a factor of 4, to F.

All three charges are returned to their original positions. What is the magnitude of the net force experienced by the charge on the right?

1. 5F
2. 4F
3. more than 3F but less than 4F
4. 3F
5. None of the above

The forces add as vectors, so 4F to the right and F to the left give a total force of 3F to the right. It's important to realize that the interaction between the negative charge and the positive charge in the center is irrelevant when we're considering the net force on the charge on the right. Also, the fact that the center charge is between the two outer charges doesn't matter. The negative charge exerts a force F on the right-most charge whether there's a charge between them or not.