**Problem 3:** Figure 4 shows a wire composed of two equal-diameter segments with conductivities \( \sigma_1 \) and \( \sigma_2 \). When current \( I \) passes through the wire, a thin layer of charge appears at the boundary between the segments. Compute the surface charge density \( \eta \) on the boundary. **Diagram:** - The diagram illustrates a cylindrical wire with two segments, labeled \( \sigma_1 \) and \( \sigma_2 \), with arrows denoting the direction of the current \( I \). Between the segments, a surface charge density \( \eta \) is indicated. **(a) Instructions:** - In Figure 4, indicate the directions of the electric fields in each segment of the wire. Write down the expressions for the magnitudes of these electric fields, \( E_1 \) and \( E_2 \). **(b) Gaussian Surface:** - In Figure 4, draw a closed Gaussian surface that could be used to find the surface charge density \( \eta \). Assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross-section. Write down Gauss's law, \( \Phi_e = \frac{Q_{en}}{\varepsilon_0} \), for this Gaussian surface. - Pay attention to the signs of different terms in the flux (the sign is negative if the field \( \vec{E} \) makes an angle \( > 90^\circ \) with the surface area vector). Use Gauss’s law to get the expression for \( \eta \) in terms of \( I \), \( \sigma_1 \), \( \sigma_2 \), and the wire’s cross-sectional area \( A \). **(c) Calculation:** - A 1.0-mm-diameter wire made of copper and iron segments carries a 5.0 A current. How much charge accumulates at the boundary between the segments? (*Answer: deficit of 23 electrons.*)
**Problem 3:** Figure 4 shows a wire composed of two equal-diameter segments with conductivities \( \sigma_1 \) and \( \sigma_2 \). When current \( I \) passes through the wire, a thin layer of charge appears at the boundary between the segments. Compute the surface charge density \( \eta \) on the boundary. **Diagram:** - The diagram illustrates a cylindrical wire with two segments, labeled \( \sigma_1 \) and \( \sigma_2 \), with arrows denoting the direction of the current \( I \). Between the segments, a surface charge density \( \eta \) is indicated. **(a) Instructions:** - In Figure 4, indicate the directions of the electric fields in each segment of the wire. Write down the expressions for the magnitudes of these electric fields, \( E_1 \) and \( E_2 \). **(b) Gaussian Surface:** - In Figure 4, draw a closed Gaussian surface that could be used to find the surface charge density \( \eta \). Assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross-section. Write down Gauss's law, \( \Phi_e = \frac{Q_{en}}{\varepsilon_0} \), for this Gaussian surface. - Pay attention to the signs of different terms in the flux (the sign is negative if the field \( \vec{E} \) makes an angle \( > 90^\circ \) with the surface area vector). Use Gauss’s law to get the expression for \( \eta \) in terms of \( I \), \( \sigma_1 \), \( \sigma_2 \), and the wire’s cross-sectional area \( A \). **(c) Calculation:** - A 1.0-mm-diameter wire made of copper and iron segments carries a 5.0 A current. How much charge accumulates at the boundary between the segments? (*Answer: deficit of 23 electrons.*)
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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Hello, I keep getting the wrong answer for every one of the parts, I was hoping that you can help me with part A, Part B, and Part C, can you label which one is which, thank you soo so so much
Transcribed Image Text:**Problem 3:**
Figure 4 shows a wire composed of two equal-diameter segments with conductivities \( \sigma_1 \) and \( \sigma_2 \). When current \( I \) passes through the wire, a thin layer of charge appears at the boundary between the segments. Compute the surface charge density \( \eta \) on the boundary.
**Diagram:**
- The diagram illustrates a cylindrical wire with two segments, labeled \( \sigma_1 \) and \( \sigma_2 \), with arrows denoting the direction of the current \( I \). Between the segments, a surface charge density \( \eta \) is indicated.
**(a) Instructions:**
- In Figure 4, indicate the directions of the electric fields in each segment of the wire. Write down the expressions for the magnitudes of these electric fields, \( E_1 \) and \( E_2 \).
**(b) Gaussian Surface:**
- In Figure 4, draw a closed Gaussian surface that could be used to find the surface charge density \( \eta \). Assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross-section. Write down Gauss's law, \( \Phi_e = \frac{Q_{en}}{\varepsilon_0} \), for this Gaussian surface.
- Pay attention to the signs of different terms in the flux (the sign is negative if the field \( \vec{E} \) makes an angle \( > 90^\circ \) with the surface area vector). Use Gauss’s law to get the expression for \( \eta \) in terms of \( I \), \( \sigma_1 \), \( \sigma_2 \), and the wire’s cross-sectional area \( A \).
**(c) Calculation:**
- A 1.0-mm-diameter wire made of copper and iron segments carries a 5.0 A current. How much charge accumulates at the boundary between the segments? (*Answer: deficit of 23 electrons.*)
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