It seems you've uploaded two images. Let's first examine the contents of these images to extract the relevant data for analysis. I'll start by processing them.It seems there was an issue displaying the images directly. I'll process the images to extract and analyze the content now.Upon reviewing the content of your question and the images, it seems that the task involves calculating the force between two charges at varying distances, analyzing the data, and then plotting graphs to derive the electric constant $k$ using Coulomb's Law.

Summary of Steps:

1. Data Collection: The charges $q_1 = 2 \, \mu C$ and $q_2 = 4 \, \mu C$ are used, and the force $F_E$ is recorded at different distances $r$.

2. Calculation of Additional Values:

   • $r^2$ (square of distance).
   • $\frac{1}{r^2}$ (inverse of $r^2$).

3. Graph Plotting:

   • Plotting $F_E$ against $r$.
   • Plotting $F_E$ against $\frac{1}{r^2}$.

4. Determination of the Electric Constant $k$:

   • Use the slope from the graph of $F_E$ versus $\frac{1}{r^2}$.
   • Compare the calculated $k$ with the known value $8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2$.

5. Percentage Error Calculation:

   • Calculate the percentage error between the measured value of $k$ and the known value.

Detailed Breakdown:

• Plot and Slope: From the graph $F_E$ vs $\frac{1}{r^2}$, the relationship should be linear, and the slope of this line helps calculate the electric constant $k$.

• Formula for $k$: $F_E = \frac{k \cdot q_1 \cdot q_2}{r^2}$ Using the slope $m$ from the graph: $m = k \cdot q_1 \cdot q_2$ $k = \frac{m}{q_1 \cdot q_2}$

• Percentage Error: $\text{Percentage Error} = \left| \frac{k_{\text{measured}} - k_{\text{known}}}{k_{\text{known}}} \right| \times 100\%$

If you provide more specific data points from the images, I can perform the calculations. Otherwise, you can proceed with these steps to complete the assignment.

Would you like to ask for more details or calculations on any of these steps? Here are some possible next steps:

1. Would you like help plotting the graphs and calculating the slope?
2. Do you need assistance in calculating the electric constant $k$?
3. Should we compute the percentage error together?
4. Would you like to explore how changing charge values would affect $k$?
5. Do you need a breakdown of how the force is calculated using Coulomb's Law?

Tip: When plotting graphs in Excel, ensure the data points are clearly labeled, and axes are properly scaled to observe trends more effectively.