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A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Figure (a) to determine the current i within the circle. Figure (b) shows current i as a function of r². The vertical scale is set by is = 4.7 mA, and the horizontal scale is set by r,² = 4.5 mm². (a) Is the current density uniform? (b) If so, what is its magnitude?

A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Figure (a) to determine the current i within the circle. Figure (b) shows current i as a function of r². The vertical scale is set by is = 4.7 mA, and the horizontal scale is set by r,² = 4.5 mm². (a) Is the current density uniform? (b) If so, what is its magnitude?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please help with part b of number 3
**Analysis of Current Distribution in a Cylindrical Wire** A certain cylindrical wire carries current. We draw a circle of radius \( r \) around its central axis in Figure (a) to determine the current \( i \) within the circle. Figure (b) shows current \( i \) as a function of \( r^2 \). The vertical scale is set by \( i_s = 4.7 \, \text{mA} \), and the horizontal scale is set by \( r_s^2 = 4.5 \, \text{mm}^2 \). **Questions to Explore:** - (a) Is the current density uniform? - (b) If so, what is its magnitude? **Diagram Analysis:** - **Figure (a):** This figure represents a cross-section of the cylindrical wire, showing a circle of radius \( r \) centered on the axis where the current is measured. - **Figure (b):** This graph plots current \( i \) (measured in milliamperes, mA) on the vertical axis against the square of the radius \( r^2 \) (measured in square millimeters, mm\(^2\)) on the horizontal axis. The graph shows a linear relationship, which suggests uniform current density based on the proportional increase of current with \( r^2 \). **Conclusion and Input Fields:** - For part (a), based on the linearity of the graph, the current density is likely uniform. The "yes" option is selected. - For part (b), the magnitude needs to be calculated or determined, with fields available for inputting the number and selecting the appropriate units.
Transcribed Image Text:**Analysis of Current Distribution in a Cylindrical Wire** A certain cylindrical wire carries current. We draw a circle of radius \( r \) around its central axis in Figure (a) to determine the current \( i \) within the circle. Figure (b) shows current \( i \) as a function of \( r^2 \). The vertical scale is set by \( i_s = 4.7 \, \text{mA} \), and the horizontal scale is set by \( r_s^2 = 4.5 \, \text{mm}^2 \). **Questions to Explore:** - (a) Is the current density uniform? - (b) If so, what is its magnitude? **Diagram Analysis:** - **Figure (a):** This figure represents a cross-section of the cylindrical wire, showing a circle of radius \( r \) centered on the axis where the current is measured. - **Figure (b):** This graph plots current \( i \) (measured in milliamperes, mA) on the vertical axis against the square of the radius \( r^2 \) (measured in square millimeters, mm\(^2\)) on the horizontal axis. The graph shows a linear relationship, which suggests uniform current density based on the proportional increase of current with \( r^2 \). **Conclusion and Input Fields:** - For part (a), based on the linearity of the graph, the current density is likely uniform. The "yes" option is selected. - For part (b), the magnitude needs to be calculated or determined, with fields available for inputting the number and selecting the appropriate units.
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