A point particle that has a charge of 12.5 µC is located at x = 0, y = 0 and a point particle that has a charge q is located at x = 10.0 cm, y = 0. The electric force on a point particle that has a charge of 5.0 µC at x = 20.0 cm, y = 0 is -(19.7) N . Determine the charge q.

To determine the charge q, we can use Coulomb's Law, which states that the magnitude of the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Coulomb's Law equation:
F = k * (|q1| * |q2|) / r^2

where F is the magnitude of the electric force, k is Coulomb's constant (k ≈ 9.0 × 10^9 N·m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

In this case, we know the values of |q1|, |q2|, F, and r, and we need to solve for q, the charge q of the second particle.

Given:
|q1| = 12.5 µC (microcoulombs)
|q2| = 5.0 µC
F = -19.7 N (negative sign indicates the force is attractive)
r = 20.0 cm = 0.20 m (converted to meters)

Rewriting Coulomb's Law equation to solve for q2:
q2 = (F * r^2) / (k * |q1|)

Plugging in the values:
q2 = (-19.7 N * (0.20 m)^2) / (9.0 × 10^9 N·m^2/C^2 * 12.5 × 10^-6 C)

Simplifying the calculation:
q2 = (-19.7 N * 0.04 m^2) / (9.0 × 10^9 N·m^2/C^2 * 12.5 × 10^-6 C)
q2 = - 0.788 × 10^-8 C / (9.0 × 10^9 N·m^2/C^2 * 12.5 × 10^-6 C)
q2 = - 0.788 × 10^-8 C / 1.125 × 10^4 N·m^2/C^2
q2 = - 7.019 × 10^-13 C / N·m^2
q2 ≈ -7.019 × 10^-13 N·m^2/C

Therefore, the charge q of the second particle is approximately -7.019 × 10^-13 C.