Question

Figure 3.60 shows two positively charged objects (with the same charge) and one negatively charged object. What is the direction of the net electric force on the negatively charged object? If the net force is zero, state this explicitly.

Short answer

Thedirection of the total forcewill be in the negative x-direction.

Step-by-step solution

Identification of given data

There are two positively charged objects and one negatively charged object.

Concept of attractive and repulsive force

According to Coulomb’s law, two charged particle systems will exert an attractive or repulsive force towards each other if particles of the different or the same type of charges are there.

Determination of net electric force

The forces between the like charges (positive or negative) are repulsive, while for the dissimilar charges it is attractive.

From the above figure, one can see that the negative charge is equidistant from both the positive charges and exerts the forces\({\vec F_1}\;and\;{\vec F_2}\)due to the first and second charges. They are of equal magnitude due to the same amount of positive charge.

If we take the x and y components of\({\vec F_1}\;and\;{\vec F_2}\), then It is clear from the figure that the y-components will cancel out while the x-components (which are negative) will add up.

Therefore, the direction of the total force will be in the negative x-direction.