### Force Per Unit Length vs. Inverse Distance ExperimentA student measured the force per unit length between two parallel electric currents (400 mA and 600 mA, respectively) for different distances between them. The student plotted the force per unit length (in newtons per meter) as a function of the inverse distance (in inverse meters) with the goal of calculating the permeability of the vacuum, μ₀. ### Graph Description**Title:** Force per unit length (N/m) vs. inverse distance (m⁻¹)**Y-Axis:** - Label: Force per unit length (N/m)- Range: 0 to 5.0E-07 (0 - 0.000000500 N/m)- Marks every 5.0E-08 (0.000000050 N/m)**X-Axis:** - Label: Inverse distance (m⁻¹)- Range: 0 to 12- Marks every 2 units### Data RepresentationThe graph features data points plotted with red squares and connected by a black line representing the trend. The upward trend in the graph suggests a positive relationship between the force per unit length and the inverse distance.### Trendline and EquationThe graph has a linear trendline and its equation is:\[ y = 4.66 \times 10^{-8} x \]This indicates that the force per unit length increases linearly with inverse distance, which is consistent with theoretical predictions about the force between parallel currents being inversely proportional to the distance between them.### SummaryBy analyzing the slope of the trendline, the student can utilize this relationship to calculate the permeability of vacuum, μ₀, reinforcing key concepts in electromagnetism. ### Graph Analysis and Permeability of Vacuum**Graph Explanation:**The provided image includes a graph and a subsequent question based on it. - **X-Axis (Horizontal):** This axis represents some independent variable, likely measurement points or time intervals.- **Y-Axis (Vertical):** This axis represents a dependent variable with very small values, possibly indicating some physical measurement related to magnetic fields or currents (e.g., magnetic permeability).- **Data Points:** The graph shows several data points represented by small squares. These points exhibit a linear trend, implying a proportional relationship between the variables on the x- and y-axes.The graph line indicates a linear fit, which suggests that the relationship between the variables can be described by a simple linear equation. **Question and Answer Choices:**Based on the visual data from the experiment, the task is to identify the permeability of the vacuum from the provided answer choices.**Question:***Based on this experiment, the permeability of the vacuum is:*- ○ 4.2 x π x 10^-7 T m/A- ○ 3.9 x π x 10^-7 T m/A- ○ 3.8 x π x 10^-7 T m/A- ○ 3.7 x π x 10^-7 T m/A- ○ 3.6 x π x 10^-7 T m/A- ○ 4.1 x π x 10^-7 T m/A- ○ 4.0 x π x 10^-7 T m/AThe goal here is to interpret the graph and identify which of the given values correctly represents the permeability of the vacuum (denoted as a product of a constant "π" and a power of ten).### Explanation:The permeability of free space (the vacuum) is traditionally represented by the constant \( \mu_0 \) which is approximately \( 4\pi \times 10^{-7} \) T m/A. Therefore, the correct choice should reflect this constant:- **Answer:** ○ 4.0 x π x 10^-7 T m/AThis matches the known physical constant for vacuum permeability.

Answered: Image /qna-images/answer/9009b73f-45c4-4567-a50c-24b4696fe03c.jpg

A student measured the force per unit length between two parallel electric currents (400 mA and 600 mA, respectively) for different distances between them. The student plotted the force per unit length (in newtons per meter) as a function of the inverse distance (in inverse meters) with the goal of calculating the permeability of the vacuum, µo. The graph, including the trendline, is shown in the figure below. Force per unit length (N/m) vs. inverse distance (m1) 0.0000005 4.5E-07 y = 4.66E-08x 0.0000004 3.SE-07 0.0000003 2.5E-07 0.0000002 1.SE-07 0.0000001 SE-08 2 8. 10 12

A student measured the force per unit length between two parallel electric currents (400 mA and 600 mA, respectively) for different distances between them. The student plotted the force per unit length (in newtons per meter) as a function of the inverse distance (in inverse meters) with the goal of calculating the permeability of the vacuum, µo. The graph, including the trendline, is shown in the figure below. Force per unit length (N/m) vs. inverse distance (m1) 0.0000005 4.5E-07 y = 4.66E-08x 0.0000004 3.SE-07 0.0000003 2.5E-07 0.0000002 1.SE-07 0.0000001 SE-08 2 8. 10 12

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter2: Kinematics

Section: Chapter Questions

Problem 15PE: The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit...

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