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The problem involves calculating the resultant force acting on point \( C \) due to charges at points \( A \) and \( B \), as well as the direction of the resultant force. Here's how we can approach the solution:

### Given Data:

- Triangle \( ABC \), where \( q_A = q_B = 10^{-9} \, C \), \( q_C = 5 \times 10^{-11} \, C \).
- Distance \( AB = 8 \, cm = 0.08 \, m \), and \( AC = BC = 5 \, cm = 0.05 \, m \).
- You need to determine the resultant force at point \( C \) due to charges at points \( A \) and \( B \), and the direction of the force.

### Step-by-step Solution:

#### 1. Force Between Two Charges

The electrostatic force between two point charges is given by Coulomb's law:

\[
F = k \cdot \frac{|q_1 \cdot q_2|}{r^2}
\]

where:
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the charges,
- \( r \) is the distance between the charges.

##### Forces on \( C \):

- The force due to charge at \( A \) on \( C \):
  \[
  F_{CA} = k \cdot \frac{|q_A \cdot q_C|}{AC^2}
  \]
  \[
  F_{CA} = 9 \times 10^9 \cdot \frac{10^{-9} \cdot 5 \times 10^{-11}}{(0.05)^2}
  \]
  
- The force due to charge at \( B \) on \( C \):
  \[
  F_{CB} = k \cdot \frac{|q_B \cdot q_C|}{BC^2}
  \]
  \[
  F_{CB} = 9 \times 10^9 \cdot \frac{10^{-9} \cdot 5 \times 10^{-11}}{(0.05)^2}
  \]

Since \( AC = BC \), both forces will have the same magnitude. Now, we calculate the magnitude of these forces.

#### 2. Calculate \( F_{CA} \) and \( F_{CB} \)

Let me calculate these values for you.The forces \( F_{CA} \) and \( F_{CB} \) both have a magnitude of \( 1.8 \times 10^{-7} \, \text{N} \).

#### 3. Determine the Resultant Force at \( C \)

Since the triangle is isosceles (\( AC = BC \)), the forces from charges \( A \) and \( B \) will have components along the horizontal and vertical directions. We can calculate the resultant force by considering these components.

- The horizontal components of \( F_{CA} \) and \( F_{CB} \) will cancel each other out because they are equal in magnitude but opposite in direction.
- The vertical components will add up.

The angle between the line connecting \( A \) and \( C \) (or \( B \) and \( C \)) and the horizontal is:

\[
\theta = \arccos\left(\frac{AB/2}{AC}\right) = \arccos\left(\frac{0.08/2}{0.05}\right)
\]

The vertical component of each force is \( F_{CA} \cdot \sin(\theta) \).

Let me calculate the angle \( \theta \) and the resultant force.The angle \( \theta \) between the lines \( AC \) (or \( BC \)) and the horizontal is approximately \( 36.87^\circ \).

The resultant vertical force at point \( C \) is \( 2.16 \times 10^{-7} \, \text{N} \).

#### 4. Direction of the Resultant Force
Since the horizontal components cancel out, the resultant force is directed straight upwards, perpendicular to the base \( AB \).

### Final Answer:
- The resultant force on point \( C \) due to charges \( A \) and \( B \) is \( 2.16 \times 10^{-7} \, \text{N} \), directed vertically upwards.

Would you like more details on any step, or further explanation?

Here are 5 related questions to expand your understanding:
1. How would the result change if the charge at \( A \) or \( B \) were different?
2. What would happen if the distances between the points were not equal?
3. How does Coulomb's law apply in different dielectric mediums?
4. How can we calculate the electric potential at point \( C \) due to \( A \) and \( B \)?
5. What is the significance of vector addition in calculating forces in such configurations?

**Tip**: Always break down forces into components when dealing with multiple directions to simplify calculations.

Tentukan gaya resultan pada titik C karena muatan A dan B, serta arah resultan gaya di C dalam konfigurasi segitiga ABC dengan muatan q_A, q_B, dan q_C, serta jarak yang diberikan.

Calculate the resultant force on point C due to charges at A and B in a triangle configuration. This problem applies Coulomb's Law and vector addition to determine the magnitude and direction of the force. Suitable for high school physics students.

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