Three point charges are fixed on the x-axis: 8.7×10^−6 C at x = −0.68 m, −3.0×10^−6 C at the origin, and 2.6×10^−6 C at x = 0.65 m. Find the electrostatic force acting on the charge at the origin due to the other two charges. Let a positive value indicate a force in the positive x direction, and a negative value indicate a force in the negative x direction.

The + charge at -.68 pulls the charge at the origin left (-)

The + charge at +.65 pulls the origin right (+)
so
F = k*10^-12 (2.6/.65^2 -8.7/.68^2)(3.0)

To find the electrostatic force acting on the charge at the origin due to the other two charges, we can use the principle of superposition. This principle states that the total force on a charge due to multiple other charges is the vector sum of the individual forces due to each charge.

The electrostatic force between two charges is given by Coulomb’s Law:

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

Where:
F is the electrostatic force between the charges,
k is the electrostatic constant (k = 8.99 × 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.

Let's break down the problem step by step:

1. Calculate the force between the charge at the origin and the charge at x = -0.68 m.
- The distance between them is: r1 = 0.68 m (since it's on the negative x-axis)
- The charges are: q1 = -3.0 × 10^(-6) C and q2 = 8.7 × 10^(-6) C
- Apply Coulomb's Law to find the force, F1:
F1 = k * (q1 * q2) / r1^2

2. Calculate the force between the charge at the origin and the charge at x = 0.65 m.
- The distance between them is: r2 = 0.65 m (since it's on the positive x-axis)
- The charges are: q1 = -3.0 × 10^(-6) C and q2 = 2.6 × 10^(-6) C
- Apply Coulomb's Law to find the force, F2:
F2 = k * (q1 * q2) / r2^2

3. Calculate the net force by adding the individual forces together:
- Since the charges at x = -0.68 m and x = 0.65 m both have positive magnitudes, we need to consider the direction of the force as well.
- Use the equation: Net force = F2 - F1. (Subtracting F1 because it acts in the negative x direction)
- The resulting net force will give us the direction and magnitude of the force acting on the charge at the origin.

Remember that in Coulomb's Law, the force can be negative or positive, indicating the direction along the x-axis.

Plug in the values for the equation and calculate the net force to get the final result.