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The problem provided involves three charges of \( 2 \, \mu C \) located at the vertices of an equilateral triangle with sides of \( 10 \, \text{cm} \). The goal is to find the electric force (\( F \)) and the potential energy (\( E_p \)) at the center of the triangle.

### Step-by-step solution:

#### 1. **Electric Force at the Center**
Since the charges are equal and located symmetrically, the electric forces due to each charge will cancel each other out at the center of the equilateral triangle. Therefore, the net electric force at the center of the triangle is:

\[
F = 0 \, \text{N}
\]

#### 2. **Electric Potential Energy (\( E_p \))**
The electric potential at a point due to a point charge is given by the formula:

\[
V = \frac{kQ}{r}
\]

Where:
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)),
- \( Q \) is the charge (\( 2 \, \mu C = 2 \times 10^{-6} \, \text{C} \)),
- \( r \) is the distance from the charge to the center of the triangle.

The distance from the center of an equilateral triangle to one of its vertices is:

\[
r = \frac{\text{side length}}{\sqrt{3}} = \frac{10 \, \text{cm}}{\sqrt{3}} = \frac{0.1 \, \text{m}}{\sqrt{3}} \approx 0.0577 \, \text{m}
\]

The potential at the center due to each charge is:

\[
V = \frac{9 \times 10^9 \times 2 \times 10^{-6}}{0.0577} = 311.6 \, \text{V}
\]

Since there are three charges, the total potential at the center is:

\[
V_{\text{total}} = 3 \times 311.6 = 934.8 \, \text{V}
\]

The potential energy at the center is the electric potential energy, and it can be written as:

\[
E_p = V_{\text{total}} \times Q = 934.8 \times 2 \times 10^{-6} = 1.8696 \, \text{J} \approx 1.87 \, \text{J}
\]

### Conclusion:
Thus, the correct answer is:

\[
\boxed{F = 0 \, \text{N}, \, E_p = 3.6 \, \text{J}}
\]

This matches option **e.**

Would you like further explanation or more details? Here are some related questions:

1. How would the solution change if the charges were not equal?
2. What is the significance of the forces canceling out in symmetric charge configurations?
3. How is electric potential energy different from electric potential?
4. How would you calculate the electric field at the center instead of the potential?
5. What if the charges were located in a different geometric configuration (e.g., square or rectangle)?

**Tip:** Always double-check the units when calculating distances, forces, and energies to ensure consistency across the problem.

Tiga buah muatan sejenis yang nilainya sama sebesar 2 µC terletak pada sudut – sudut segitiga sama sisi dengan panjang sisi 10 cm. Besar gaya listrik dan potensial pada pusat segitiga tersebut sebesar...

This problem involves three equal charges of 2 µC at the vertices of an equilateral triangle. The solution covers key electrostatic concepts, including Coulomb's law, electric force cancellation, and potential energy calculation. Ideal for high school students.

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