Let's break down the problem step by step: --- ## 1. **Understanding the ProblemGiven: - Table of Current (\(I\)) vs. Magnetic Flux (\(\Phi\)) - A graph with a best-fit line through the data points - The question asks: **What is the inductance (\(L\)) of the solenoid?** --- ## 2. **Relevant Formula** The relationship between magnetic flux (\(\Phi\)) and current (\(I\)) in a solenoid is: \[ \Phi = L \cdot I \] Where: - \(\Phi\): Magnetic flux (Wb) - \(L\): Inductance (H) - \(I\): Current (A) From this equation, the **slope** of the graph (\(\frac{\Phi}{I}\)) gives the **inductance \(L\)**. --- ## 3. **Extract Data** From the table: | Current (A) | Magnetic Flux (Wb) | |-------------|--------------------| | .375 | 1.50 | | .825 | 3.40 | | 1.25 | 5.20 | --- ## 4. **Calculate the Slope** To find the inductance \(L\), calculate the slope using two data points: Let's use the first and last points for best accuracy: - \((I_1, \Phi_1) = (.375, 1.50)\) - \((I_2, \Phi_2) = (1.25, 5.20)\) \[ \text{Slope} = L = \frac{\Delta \Phi}{\Delta I} = \frac{5.20 - 1.50}{1.25 - .375} = \frac{3.70}{.875} \approx 4.23 \, \text{H} \] --- ## 5. **Final Answer** \[ \boxed{L = 4.2 \ \text{H}} \] --- ### **Explanation** - The inductance is found from the slope of the magnetic flux vs. current graph. - Using the formula \(\Phi = L I\), the slope equals \(L\). - Calculating the slope from the provided data gives the inductance. --- **Final Answer:** \[ \boxed{4.2 \ \text{H}} \]