An object with a charge of +6.0 µC is 0.30 m from a second object and experiences an attractive force of 1.80 N. What is the magnitude of the charge on the second object? (µC = 1.0 × 10-6 C) (Answer: -3.0 µC)

The answer is provided but I don't know how to work it out.

To solve this problem, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is:

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

where:
- F is the force between the two objects,
- k is the electrostatic constant (k = 9.0 x 10^9 N m^2/C^2),
- q1 and q2 are the charges of the two objects, and
- r is the distance between the two objects.

In this problem, we are given the following information:
- Charge of the first object (q1) = +6.0 µC = +6.0 x 10^-6 C
- Distance between the two objects (r) = 0.30 m
- Force between the two objects (F) = 1.80 N

We need to find the magnitude of the charge on the second object (|q2|).

First, let's rearrange Coulomb's Law to solve for |q2|:

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

Now, substitute the given values into the equation:

|q2| = (1.80 N * (0.30 m)^2) / (9.0 x 10^9 N m^2/C^2 * 6.0 x 10^-6 C)

Simplifying the equation, we have:

|q2| = (1.80 N * 0.09 m^2) / (54.0 x 10^3 N m^2/C)

|q2| = 0.162 N m^2 / (54.0 x 10^3 N m^2/C)

|q2| = 0.003 C / (54.0 x 10^3)

|q2| = 3.0 x 10^-3 C

Finally, convert the charge from coulombs to microcoulombs:

|q2| = 3.0 x 10^-3 C = 3.0 µC

Since the answer provided is -3.0 µC, it means that the magnitude of the charge on the second object is 3.0 µC and the charge itself is negative.