To understand the behavior of the two charged balls after one is discharged, we need to consider the forces acting on them and how the discharge affects their charges. Initially, both balls are equally charged, creating a repulsive electrostatic force between them, which is balanced by the tension in the threads suspending them. When one ball is discharged, it loses its charge, and the dynamics change significantly.
Initial Conditions
Initially, both balls carry the same charge, let's say +Q. The repulsive force between them can be described by Coulomb's Law:
Where:
- F is the force between the charges.
- k is Coulomb's constant.
- Q1 and Q2 are the magnitudes of the charges.
- r is the distance between the centers of the two charges.
In equilibrium, the tension in the threads balances the electrostatic repulsion. The distance between the balls is given as a = 10 cm.
After Discharging One Ball
When one of the balls is discharged, it loses its charge and becomes neutral. Let's say Ball 1 is discharged, so it now has a charge of 0, while Ball 2 still has a charge of +Q. The electrostatic force between the two balls now becomes:
Since Ball 1 is neutral, there is no longer any repulsive force acting on it from Ball 2. The only forces acting on Ball 1 are the tension in the thread and gravity. As a result, Ball 1 will no longer be pushed away and will tend to move towards Ball 2 due to the gravitational pull.
Behavior of the Balls
As Ball 1 moves towards Ball 2, it will be influenced by the gravitational force pulling it downwards and the tension in the thread. Ball 2, still charged, will remain in its position unless acted upon by another force. The distance between the two balls will decrease as Ball 1 approaches Ball 2.
Final Equilibrium Position
Once Ball 1 comes to rest, the distance between the two balls will be determined by the length of the threads and the angle they make with the vertical. Since the length of the threads is much greater than the distance between the balls, we can assume that Ball 1 will settle directly below Ball 2. The distance b between the two balls will be effectively zero, as they will be in line vertically.
In summary, after discharging one ball, the neutral ball will move towards the charged ball due to the absence of repulsive force, and they will come to rest at a distance b that approaches zero, depending on the exact setup and any slight movements caused by external factors.
