An equilateral triangle has sides of 0.15 m. Charges of -9.4, +8.0, and +2.5 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 2.5-µC charge.

each cahrge has X10^-6 btw

Find the forces, add them as vectors.

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To find the magnitude of the net electrostatic force exerted on the 2.5 µC charge, we need to calculate the electrostatic force between each pair of charges, and then determine the vector sum of these forces.

1. Calculate the force between the 2.5 µC charge and the -9.4 µC charge:
The electrostatic force between two charges can be calculated using Coulomb's Law:

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

where F is the force between the charges, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

First, let's convert the charges from µC to C:
-9.4 µC = -9.4 x 10^-6 C
2.5 µC = 2.5 x 10^-6 C

Using Coulomb's Law,
F1 = (9 x 10^9 Nm^2/C^2) * (|(-9.4 x 10^-6 C) * (2.5 x 10^-6 C)|) / (0.15 m)^2

Calculate F1.

2. Calculate the force between the 2.5 µC charge and the +8.0 µC charge:
Using the same method as above, calculate F2.

F2 = (9 x 10^9 Nm^2/C^2) * (|(8.0 x 10^-6 C) * (2.5 x 10^-6 C)|) / (0.15 m)^2

Calculate F2.

3. Calculate the force between the -9.4 µC charge and the +8.0 µC charge:
Using the same method as above, calculate F3.

F3 = (9 x 10^9 Nm^2/C^2) * (|(-9.4 x 10^-6 C) * (8.0 x 10^-6 C)|) / (0.15 m)^2

Calculate F3.

4. Determine the vector sum of the forces:
To find the net electrostatic force, we need to calculate the resultant vector sum of F1, F2, and F3. Since these forces act on a common point, we can add them together as vectors.

F_net = F1 + F2 + F3

Calculate F_net.

The magnitude of the net electrostatic force exerted on the 2.5 µC charge is the magnitude of the vector F_net that we calculated.

To find the magnitude of the net electrostatic force exerted on the 2.5-µC charge, we need to calculate the individual forces between the charges and then add them vectorially.

The formula to calculate the electrostatic force between two charges is given by Coulomb's Law:

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

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

Let's calculate the forces between the 2.5-µC charge and the other charges.

1. Calculate the force between the 2.5-µC and the -9.4-µC charges:
F1 = (k * |q1 * q2|) / r^2
= (9 * 10^9 Nm^2/C^2) * (|2.5 * (-9.4)| * 10^-12 C^2) / (0.15m)^2

2. Calculate the force between the 2.5-µC and the +8.0-µC charges:
F2 = (k * |q1 * q2|) / r^2
= (9 * 10^9 Nm^2/C^2) * (|2.5 * 8.0| * 10^-12 C^2) / (0.15m)^2

Now, we need to find the direction of these forces. Since the charges are located at the corners of an equilateral triangle, the forces are directed along the lines connecting the charges. We can use vectors to represent these forces.

3. Represent the forces as vectors:
Let's assume that the 2.5-µC charge is at the bottom corner of the triangle, and the -9.4-µC and +8.0-µC charges are at the top left and top right corners, respectively.
F1 vector points from the 2.5-µC charge towards the -9.4-µC charge.
F2 vector points from the 2.5-µC charge towards the +8.0-µC charge.

4. Add the vectors:
To find the net force (F_net), add the vectors F1 and F2. Use vector addition rules to add the forces.

5. Calculate the magnitude of the net force:
|F_net| = sqrt(F_net_x^2 + F_net_y^2)

By following these steps, you can calculate the magnitude of the net electrostatic force exerted on the 2.5-µC charge.