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Problem 3: Fig. 4 shows a wire that is made of two equal- diameter segments with conductivities o, and 02. When current I passes through the wire, a thin layer of charge appears at the boundary between the segments. Compute the surface charge density n on the boundary. a) In Fig. 4, indicate the directions of the electric fields in each segment of the current. Write down the expressions for the magnitudes of these electric fields, E, and E₂. A I 10² Surface charge density no FIG. 4: The scheme for Problem 3 b) In Fig.4, draw a closed Gaussian surface that could be used to find the surface charge density n (you may want to revisit Example 24.6 of the textbook). Here, we do not assume the charged plane to be infinite, but we do assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross section. Write down the Gauss's law, e = in, for this Gaussian surface. Pay attention to the signs of different terms in the flux (the sign is negative if the field E makes an angle > 90° with the surface area vector). From the Gauss's law, get the expression for n in terms of I, 01, 02, and the wire's cross-sectional area A. €0 c) 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: Fig. 4 shows a wire that is made of two equal- diameter segments with conductivities o, and 02. When current I passes through the wire, a thin layer of charge appears at the boundary between the segments. Compute the surface charge density n on the boundary. a) In Fig. 4, indicate the directions of the electric fields in each segment of the current. Write down the expressions for the magnitudes of these electric fields, E, and E₂. A I 10² Surface charge density no FIG. 4: The scheme for Problem 3 b) In Fig.4, draw a closed Gaussian surface that could be used to find the surface charge density n (you may want to revisit Example 24.6 of the textbook). Here, we do not assume the charged plane to be infinite, but we do assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross section. Write down the Gauss's law, e = in, for this Gaussian surface. Pay attention to the signs of different terms in the flux (the sign is negative if the field E makes an angle > 90° with the surface area vector). From the Gauss's law, get the expression for n in terms of I, 01, 02, and the wire's cross-sectional area A. €0 c) 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
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 all of the parts from the problem I was wondering if u can help me with Part A,part b and part c, can u label them so I know which one is which because I know what I got wrong thank u

**Problem 3:** Fig. 4 shows a wire that is made 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. a) In Fig. 4, indicate the directions of the electric fields in each segment of the current. Write down the expressions for the magnitudes of these electric fields, \( E_1 \) and \( E_2 \). **Diagram Explanation:** The diagram illustrates a cylindrical wire divided into two segments, each labeled with its respective conductivity \( \sigma_1 \) and \( \sigma_2 \). The boundary between the segments is marked with a surface charge density \( \eta \). An arrow labeled \( I \) indicates the direction of the current flow through the wire from left to right. b) In Fig. 4, draw a closed Gaussian surface that could be used to find the surface charge density \( \eta \) (you may want to revisit Example 24.6 of the textbook). Here, we do not assume the charged plane to be infinite, but we do assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross section. Write down the Gauss's law, \( \Phi_e = \frac{q_{in}}{\varepsilon_0} \), 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). From the Gauss’s law, get the expression for \( \eta \) in terms of \( I \), \( \sigma_1 \), \( \sigma_2 \), and the wire’s cross-sectional area \( A \). c) 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.)
Transcribed Image Text:**Problem 3:** Fig. 4 shows a wire that is made 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. a) In Fig. 4, indicate the directions of the electric fields in each segment of the current. Write down the expressions for the magnitudes of these electric fields, \( E_1 \) and \( E_2 \). **Diagram Explanation:** The diagram illustrates a cylindrical wire divided into two segments, each labeled with its respective conductivity \( \sigma_1 \) and \( \sigma_2 \). The boundary between the segments is marked with a surface charge density \( \eta \). An arrow labeled \( I \) indicates the direction of the current flow through the wire from left to right. b) In Fig. 4, draw a closed Gaussian surface that could be used to find the surface charge density \( \eta \) (you may want to revisit Example 24.6 of the textbook). Here, we do not assume the charged plane to be infinite, but we do assume that the electric field is (i) uniform across the wire and (ii) directed along the wire, perpendicular to its cross section. Write down the Gauss's law, \( \Phi_e = \frac{q_{in}}{\varepsilon_0} \), 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). From the Gauss’s law, get the expression for \( \eta \) in terms of \( I \), \( \sigma_1 \), \( \sigma_2 \), and the wire’s cross-sectional area \( A \). c) 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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