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Calculate the net force on the left charge due to the other two. Enter a positive value if the force is directed to the right and a negative value if the force is directed to the left.
Express your answer to two significant figur

To calculate the net force on the left charge (\(+65 \, \mu C\)) due to the other two charges, we need to use Coulomb's Law:

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

Where:
- \(F\) is the magnitude of the force between two charges,
- \(k_e = 8.99 \times 10^9 \, \text{N}\cdot \text{m}^2/\text{C}^2\) is Coulomb's constant,
- \(q_1\) and \(q_2\) are the magnitudes of the charges, and
- \(r\) is the distance between the charges.

### Step 1: Forces Between the Left Charge and Each of the Other Charges
1. **Force between the left charge (\(+65 \, \mu C\)) and the middle charge (\(+48 \, \mu C\)):**
   - The distance is \(L\).
   - The force will be repulsive because both charges are positive.

   Using Coulomb's law:
   \[
   F_1 = k_e \frac{|65 \times 10^{-6} \cdot 48 \times 10^{-6}|}{L^2}
   \]

2. **Force between the left charge (\(+65 \, \mu C\)) and the right charge (\(-95 \, \mu C\)):**
   - The distance is \(2L\) (since the total distance between these two charges is twice the distance \(L\)).
   - The force will be attractive because the charges are of opposite signs.

   Using Coulomb's law:
   \[
   F_2 = k_e \frac{|65 \times 10^{-6} \cdot 95 \times 10^{-6}|}{(2L)^2}
   \]

### Step 2: Calculate the Net Force
The forces \(F_1\) and \(F_2\) are in opposite directions. Since we are asked to find the net force on the left charge and define right as positive:
- \(F_1\) pushes to the right (positive direction),
- \(F_2\) pulls to the left (negative direction).

The net force is:
\[
F_{\text{net}} = F_1 - F_2
\]

Let me compute these forces now.The net force on the left charge due to the other two charges is approximately \( 14.17 \, \text{N} \), directed to the right (positive direction).

Would you like more details on any part of the solution? Here are some related questions you might find useful:

1. How do we determine the direction of the force between two charges?
2. What happens if the charges are of opposite signs?
3. How do we handle forces in a system with more than two charges?
4. What if the distances between charges were different?
5. Can you explain Coulomb's constant in more detail?

**Tip:** Always remember to check both the magnitude and direction of forces when working with multiple charges.

Calculate the net force on the left charge due to the other two. Enter a positive value if the force is directed to the right and a negative value if the force is directed to the left.

Learn how to calculate the net force on a charge using Coulomb's law in a system of three charges. This problem involves electrostatics, charge interactions, and distances between charges. Suitable for Grades 10-12.

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