please help :/

Three charges are fixed to an xy coordinate system. A charge of +25C is on the y axis at y = +2.7 m. A charge of -16C is at the origin. Lastly, a charge of +66C is on the x axis at x = +2.7 m. Determine (a) the magnitude and (b) direction of the net electrostatic force on the charge at x = +2.7 m. Specify the direction as a positive angle relative to the +x axis.

8e-21

To determine the magnitude and direction of the net electrostatic force on the charge at x = +2.7 m, we can use Coulomb's law. Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's start by calculating the magnitude of the individual forces exerted on the charge at x = +2.7 m due to the other two charges.

1. Calculate the force between the charge at x = +2.7 m and the charge at the origin:
- Charge at x = +2.7 m (q1) = +66 C
- Charge at the origin (q2) = -16 C
- Distance (r) = 2.7 m

Using Coulomb's law formula:
F1 = (k * |q1 * q2|) / r^2

Here, k is the electrostatic constant which equals 9 x 10^9 Nm^2/C^2.

Plugging in the values:
F1 = (9 x 10^9 * |66 * (-16)|) / (2.7)^2

2. Calculate the force between the charge at x = +2.7 m and the charge on the y-axis:
- Charge at x = +2.7 m (q1) = +66 C
- Charge on the y-axis (q2) = +25 C
- Distance (r) = 2.7 m

Using Coulomb's law formula:
F2 = (k * |q1 * q2|) / r^2

Plugging in the values:
F2 = (9 x 10^9 * |66 * 25|) / (2.7)^2

3. Find the net force by considering both forces:
- Since forces are vector quantities, they have magnitude and direction. The net force is the vector sum of the individual forces.
- Since the two forces are at right angles to each other (one along the x-axis and the other along the y-axis), we can use vector addition.
- The magnitude of the net force can be found using the Pythagorean theorem:
F_net = √(F1^2 + F2^2)

The direction of the net force can be found using trigonometry:
θ = atan(F2 / F1)

Here, atan represents the inverse tangent function.

Now that we have outlined the steps, you can use these formulas to calculate the magnitude and direction of the net electrostatic force on the charge at x = +2.7 m.