Answer:

Explanation:

When two identical metal balls with charges 2Q and -Q are separated by some distance, they exert a force f on each other. Let's consider that the distance between the balls is d.

1. Calculation of force f
The force f between the two metal balls can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically,

f = k * (2Q) * (-Q) / d^2

where k is the Coulomb's constant.

By substituting the values of k, 2Q, -Q, and d, we get

f = -2kQ^2 / d^2

2. Joining the metal balls with a conducting wire
When the two metal balls are joined by a conducting wire, they become like a single ball with a charge of 3Q. This is because the charges on the metal balls are free to move, and they will redistribute themselves until they are evenly distributed throughout the surface of the metal balls.

3. Removing the conducting wire
When the conducting wire is removed, the charges on the metal balls will redistribute themselves again. However, this time the charges on the metal balls will not be evenly distributed because the metal balls have different charges.

The charge on the positively charged metal ball will be less than 3Q, and the charge on the negatively charged metal ball will be more than -3Q. Let's assume that the charge on the positively charged metal ball is q1 and the charge on the negatively charged metal ball is q2.

4. Calculation of the force between the metal balls
The force between the metal balls can be calculated using Coulomb's law again. Mathematically,

F = k * q1 * q2 / d^2

where k is the Coulomb's constant.

By substituting the values of k, q1, q2, and d, we get

F = k * (3Q - q1) * (3Q + q2) / d^2

By simplifying this equation, we get

F = 9kQ^2 / d^2 - kq1q2 / d^2

The first term in this equation is the force between two metal balls when they are joined by a conducting wire. The second term is the force between two metal balls when they are not joined by a conducting wire.

5. Determining the magnitude of force between the metal balls
The magnitude of the force between the metal balls is given by

|F| = |9kQ^2 / d^2 - kq1q2 / d^2|

We know that q1 + q2 = 3Q because the total charge on the metal balls is still 3Q. By substituting q2 = 3Q - q1 in the above equation, we get

|F| = |9kQ^2 / d^2 - 3kQq1 / d^2 + kq1^2 / d^2|

By differentiating this equation with respect to q1 and equating it to zero, we can find the value of q1 that minimizes the force. This value turns out to be q1 = Q/2.

By substit

When connected via a conducting wire , to balance out the potential difference electron flow to the 1st ball . Then both will have Q|2 charge each .