Initial Analysis

We are given that two similar spheres, when placed 2 cm apart, attract each other with a force of 4 dyne. After connecting the spheres with a wire, they now repel each other with a force of 2.25 dyne. We need to calculate the initial charge on the spheres, neglecting the capacity of the wire.

Electrostatic Force

The force between two charged objects is given by Coulomb's Law:

F = k * (q1 * q2) / r^2

Where F is the electrostatic force, k is the electrostatic constant, q1 and q2 are the charges on the objects, and r is the distance between the objects.

Attractive Force

When the spheres are 2 cm apart, they attract each other with a force of 4 dyne. Let's denote the initial charges on the spheres as q1 and q2.

Using Coulomb's Law, we can write the equation for the attractive force:

4 = k * (q1 * q2) / (0.02)^2

Simplifying the equation, we get:

0.0008 = (q1 * q2)

Repulsive Force

When the spheres are connected by a wire, they repel each other with a force of 2.25 dyne. The charges on the spheres are now denoted as q1' and q2'.

Using Coulomb's Law again, we can write the equation for the repulsive force:

2.25 = k * (q1' * q2') / (0.02)^2

Simplifying the equation, we get:

0.0009 = (q1' * q2')

Calculating Initial Charges

Since we know that the spheres are similar, their charges should be equal initially (q1 = q2). Similarly, after connecting them with a wire, their charges should still be equal (q1' = q2').

Therefore, we can substitute q1 = q2 and q1' = q2' into the equations:

0.0008 = (q1 * q2)

0.0009 = (q1 * q2)

Since the charges are the same in both cases, we can equate the two equations:

0.0008 = 0.0009

This is not possible, which means there is no consistent solution for the charges on the spheres that satisfies both the attractive and repulsive forces.

Conclusion

Based on the given information, there is no consistent solution for the initial charges on the spheres that can explain both the attractive and repulsive forces. It is possible that there is some additional factor or information missing that would allow us to find a consistent solution.