Final answer:
The second charge q that results in an attractive force of 0.20 N with a first charge of 9.0 μC located at the origin is approximately 2.22 μC, as calculated using Coulomb's Law.
Step-by-step explanation:
To find the charge q on the second charge positioned on the x-axis that results in a magnitude of the attractive force of 0.20 N between it and another charge of 9.0 μC located at the origin, we use Coulomb's Law. Coulomb's Law states that the force (F) between two point charges is proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them.
Using the formula F = k * |q1 * q2| / r^2, where k is Coulomb's constant (approximately 8.99 × 10^9 N·m^2/C^2), we can solve for the unknown charge q. Plugging in the known values:
F = (8.99 × 10^9 N·m^2/C^2) * |9.0 × 10^-6 C * q| / (1.0 m)^2
Solving for q gives us:
q = F * r^2 / (k * 9.0 × 10^-6 C)
0.20 N * (1.0 m)^2 / (8.99 × 10^9 N·m^2/C^2 * 9.0 × 10^-6 C) = q
q ≈ 2.22 × 10^-6 C or 2.22 μC
Therefore, the charge q is approximately 2.22 μC.