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The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances , (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances , (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances , (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

please put the units 

**Electric Field of a Spherical Shell with a Spherical Cavity:** The diagram presents a spherical shell with a central spherical cavity. The shell is uniformly filled with positive charge. Let's break down the features of this illustration in detail: 1. **Outer Shell**: - This is the outermost part of the diagram, represented as a large circle. - The area within this large circle is dotted with plus signs (+), indicating that the shell is uniformly positively charged. - This outer shell has a radius of \( b \). 2. **Inner Cavity**: - Inside the outer shell, there is a smaller circle representing a cavity with radius \( a \). - The cavity itself is empty and lacks any charge representation within it. 3. **Radiuses**: - The distance from the center of the cavity to its boundary is labeled as \( a \). - The distance from the center of the cavity to the boundary of the outer shell is labeled as \( b \). 4. **Electric Field**: - The uniform distribution of positive charges in the shell suggests a specific structure to the electric field. - Within the cavity (radius less than \( a \)), due to symmetry and the lack of charge inside the cavity, the electric field is zero. - Outside the cavity but within the shell (radius between \( a \) and \( b \)), the electric field distributes according to the shell's charge. - Beyond the outer radius \( b \), the field behaves as if all the charge were concentrated at the center of the sphere. 5. **Applications**: - This setup helps illustrate concepts like Gauss’s Law in electrodynamics, and is especially useful for understanding electric fields in symmetric charge distributions. - This model serves as a fundamental example for analyzing fields in more complicated charge configurations.
Transcribed Image Text:**Electric Field of a Spherical Shell with a Spherical Cavity:** The diagram presents a spherical shell with a central spherical cavity. The shell is uniformly filled with positive charge. Let's break down the features of this illustration in detail: 1. **Outer Shell**: - This is the outermost part of the diagram, represented as a large circle. - The area within this large circle is dotted with plus signs (+), indicating that the shell is uniformly positively charged. - This outer shell has a radius of \( b \). 2. **Inner Cavity**: - Inside the outer shell, there is a smaller circle representing a cavity with radius \( a \). - The cavity itself is empty and lacks any charge representation within it. 3. **Radiuses**: - The distance from the center of the cavity to its boundary is labeled as \( a \). - The distance from the center of the cavity to the boundary of the outer shell is labeled as \( b \). 4. **Electric Field**: - The uniform distribution of positive charges in the shell suggests a specific structure to the electric field. - Within the cavity (radius less than \( a \)), due to symmetry and the lack of charge inside the cavity, the electric field is zero. - Outside the cavity but within the shell (radius between \( a \) and \( b \)), the electric field distributes according to the shell's charge. - Beyond the outer radius \( b \), the field behaves as if all the charge were concentrated at the center of the sphere. 5. **Applications**: - This setup helps illustrate concepts like Gauss’s Law in electrodynamics, and is especially useful for understanding electric fields in symmetric charge distributions. - This model serves as a fundamental example for analyzing fields in more complicated charge configurations.
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