Two objects carry initial charges that are q1 and q2, respectively, where |q2| > |q1|. they are located 0.160 m apart and behave like point charges. they attract each other with a force that has a magnitude of 1.30 n. the objects are then brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. now it is found that the objects repel one another with a force whose magnitude is equal to the magnitude of the initial attractive force. what are the magnitudes of the initial charges on the objects?

Explanation:

According to the Coulomb's law, the magnitude of the electrostatic force between two static point charges   and , separated by a distance , is given by

where k is the Coulomb's constant.

Initially,

The negative sign is taken with force F because the force is attractive.

Therefore, the initial electrostatic force between the charges is given by

Now, the objects are then brought into contact, so the net charge is shared equally, and then they are returned to their initial positions.

The force is now repulsive, therefore,

The new charges on the two objects are

The new force is given by

Using (1),

Using (1),

When ,

When ,

Since,

Therefore,