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The question in the image asks to find the Coulomb force acting on point C, given that the charge at point C is \( 3 \, \mu C \), and there are two other charges in the system: \( +6 \, \mu C \) at point A and \( -2 \, \mu C \) at point B. The distances are as follows:

- Distance between A and C: 6 cm
- Distance between A and B: 8 cm
- Distance between B and C: Needs to be calculated using the Pythagorean theorem.

### Steps to solve the problem:

1. **Calculate the distance between points B and C:**

   Using the Pythagorean theorem:
   \[
   BC = \sqrt{(AC)^2 + (AB)^2} = \sqrt{(6 \, \text{cm})^2 + (8 \, \text{cm})^2}
   \]

2. **Use Coulomb's Law** to find the force between each pair of charges:

   Coulomb's Law is given by:
   \[
   F = k \frac{|q_1 \cdot q_2|}{r^2}
   \]
   where:
   - \( k \) is Coulomb's constant \( (9 \times 10^9 \, \text{Nm}^2/\text{C}^2) \),
   - \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
   - \( r \) is the distance between the charges.

3. **Determine the direction of each force**:
   - The force due to \( +6 \, \mu C \) at point A will repel the charge at C.
   - The force due to \( -2 \, \mu C \) at point B will attract the charge at C.
   - The total force on point C will be the vector sum of these forces.

Let me calculate step 1 first.The distance between points B and C is \( 10 \, \text{cm} \).

Now, let's proceed by calculating the forces between the charges at point C and the charges at points A and B using Coulomb's law. We will convert the distances to meters and use the charge values:

- Charge at A: \( +6 \, \mu C \)
- Charge at B: \( -2 \, \mu C \)
- Charge at C: \( 3 \, \mu C \)

Distances:
- \( AC = 0.06 \, \text{m} \)
- \( BC = 0.10 \, \text{m} \)

Next, we will compute the forces.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still follow the steps outlined above to solve the problem manually:

1. Use Coulomb's Law to find the forces between charges at C and A, and C and B:
   \[
   F = k \frac{|q_1 \cdot q_2|}{r^2}
   \]
   where \( q_1 \) and \( q_2 \) are the charge values in coulombs, \( r \) is the distance in meters, and \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).

2. Calculate the force for \( F_{AC} \) using the distance between A and C (0.06 meters) and for \( F_{BC} \) using the distance between B and C (0.10 meters).

3. Add the forces as vectors since they act in different directions.

If you want to proceed with this calculation manually or need further help, feel free to ask.

Would you like additional details, or do you have any questions about the steps?

Here are 5 related questions for further practice:
1. How would the forces change if the charge at point A were doubled?
2. What would happen to the force if the distance between points A and C were halved?
3. How do you calculate the net force in a system of three charges?
4. How does Coulomb's law compare to gravitational force between masses?
5. What is the significance of the sign of the charges when calculating force?

**Tip:** Always make sure to convert units to SI units (meters, coulombs) when working with Coulomb's law.

Berapakah gaya Coulomb pada titik C jika muatan pada titik C 3μC? Diberikan muatan +6μC di titik A dan -2μC di titik B. Jarak antara A dan C adalah 6 cm, dan jarak antara A dan B adalah 8 cm.

Learn how to calculate the Coulomb force on point C, given that point C has a charge of 3μC, point A has a charge of +6μC, and point B has a charge of -2μC. The distances between A and C are 6 cm, and between A and B are 8 cm. Includes detailed steps involving Coulomb's Law and the Pythagorean Theorem.

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