Two identical conducting spheres, fixed in place, attract each other with a force of 0.114 N when their center to center separation is 45.00 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres have a net positive charge and repel each other with an electrostatic force of 0.044 N. What was the initial negative charge on one of the spheres, and what was the initial positive charge on the other?(Hint: Use charge conservation and solve for one of the initial charges. You will end up with a quadratic equation. The solutions give you the positive and negative charges.)

I've done all of this, and I have the initial positive charge, which is 2.88199e-6 Coulombs. But I can't get the initial negative charge. Nothing that I do will give me the correct answer. Do you have any ideas?

To find the initial negative charge on one of the spheres, we can follow these steps:

1. Let's assume that the initial negative charge on one of the spheres is denoted as Q1 (in Coulombs) and the positive charge on the other sphere is denoted as Q2 (in Coulombs).

2. We know that the spheres are identical, so their charges must have been equal in magnitude before they were connected by a wire.

3. From the information given, when the spheres were fixed in place, they attracted each other with a force of 0.114 N. We can use Coulomb's law to relate this force to the charges and the distance between the spheres.

Coulomb's law states that the force between two charged objects is given by:

F = k * |Q1 * Q2| / r^2

Where:
F is the force between the charges (0.114 N in this case).
k is the electrostatic constant (8.99 x 10^9 N m^2/C^2).
|Q1 * Q2| is the magnitude of the product of the charges.
r is the distance between the charges (45.00 cm or 0.45 m in this case).

4. Substituting the given values into Coulomb's law, we have:

0.114 = (8.99 x 10^9) * |Q1 * Q2| / (0.45^2)

5. Simplifying the equation, we have:

|Q1 * Q2| = (0.114 * 0.45^2) / (8.99 x 10^9)

6. Now, since the charges are of opposite sign (one negative and one positive), we can write:

|Q1 * Q2| = Q1 * (-Q1) = -Q1^2

7. Substituting this back into our equation, we have:

-Q1^2 = (0.114 * 0.45^2) / (8.99 x 10^9)

8. Solving for Q1, we can take the square root of both sides of the equation:

Q1 = sqrt((0.114 * 0.45^2) / (8.99 x 10^9))

Please calculate this expression to find the value of Q1.