Two point charges of -86.5 mC and 36.3 mC are held fixed on an x axis at the origin and x = 24.4 cm, respectively. What are the magnitude and direction of the total electrostatic force on a third charge of 18.8 mC placed at

(a) x = 48.8 cm
(b) x = 97.6 cm

I've tried everything, and it seems I can't get the correct answers.

Do each individually, then add (or subtract) the two vectors

F = kq1q2/r^2
for example for a)
F = 9e9(86.5e-3)(18.8e-3)/.488^2 pulling towards negative x direction
now do it for the 36.3e-3 charge which also pushes towards the negative x direction.

To find the magnitude and direction of the total electrostatic force on the third charge, we can use Coulomb's Law. The formula for the electrostatic force between two point charges is given by:

F = (k * |q1 * q2|) / r²

Where:
F is the magnitude of the electrostatic force,
k is Coulomb's constant, approximately equal to 9 × 10^9 Nm²/C²,
q1 and q2 are the charges,
|r| is the distance between the charges.

Let's calculate the electrostatic force for each scenario.

(a) For x = 48.8 cm:

1. Find the distance between the third charge and the first charge:
r1 = x - 0 = 48.8 cm = 0.488 m

2. Calculate the electrostatic force between the third charge and the first charge:
F1 = (k * |18.8 mC * -86.5 mC|) / (0.488 m)²

3. Find the distance between the third charge and the second charge:
r2 = x - 24.4 cm = 24.4 cm = 0.244 m

4. Calculate the electrostatic force between the third charge and the second charge:
F2 = (k * |18.8 mC * 36.3 mC|) / (0.244 m)²

5. Calculate the total electrostatic force on the third charge:
F_total = F1 + F2

(b) For x = 97.6 cm:

1. Find the distance between the third charge and the first charge:
r1 = x - 0 = 97.6 cm = 0.976 m

2. Calculate the electrostatic force between the third charge and the first charge:
F1 = (k * |18.8 mC * -86.5 mC|) / (0.976 m)²

3. Find the distance between the third charge and the second charge:
r2 = x - 24.4 cm = 73.2 cm = 0.732 m

4. Calculate the electrostatic force between the third charge and the second charge:
F2 = (k * |18.8 mC * 36.3 mC|) / (0.732 m)²

5. Calculate the total electrostatic force on the third charge:
F_total = F1 + F2

By following these steps and substituting the given values into the formulas, you should be able to calculate the magnitude and direction of the total electrostatic force for both scenarios.