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We have said that Gauss's law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. a) Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss's law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)? Why or why not? b) Can we use it for a uniformly charged ring? a uniformly charged cube? Why or why not? c) Summarize the key features for each of the possible distributions when the charge density is uniform throughout the sphere, cylinder or plate by filling out the table below answering the following questions: What is the shape of the test surface? What variable do we (or the text) usually use to indicate the test point location? Which parts of that test surface have nonzero electric flux through them? What is the result of the electric field magnitude, in terms of the test point variable you identified? Almost all of these are done in the text, class and/ lab tutorial, or you can find all of them by searching the web. source shape sphere, inside sphere, outside infinite cylinder, inside infinite cylinder, outside infinite plate test surface shape test point at nonzero flux through... E is

We have said that Gauss's law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. a) Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss's law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)? Why or why not? b) Can we use it for a uniformly charged ring? a uniformly charged cube? Why or why not? c) Summarize the key features for each of the possible distributions when the charge density is uniform throughout the sphere, cylinder or plate by filling out the table below answering the following questions: What is the shape of the test surface? What variable do we (or the text) usually use to indicate the test point location? Which parts of that test surface have nonzero electric flux through them? What is the result of the electric field magnitude, in terms of the test point variable you identified? Almost all of these are done in the text, class and/ lab tutorial, or you can find all of them by searching the web. source shape sphere, inside sphere, outside infinite cylinder, inside infinite cylinder, outside infinite plate test surface shape test point at nonzero flux through... E is

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We have said that Gauss's law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. a) Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss's law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)? Why or why not? b) Can we use it for a uniformly charged ring? a uniformly charged cube? Why or why not? c) Summarize the key features for each of the possible distributions when the charge density is uniform throughout the sphere, cylinder or plate by filling out the table below answering the following questions: What is the shape of the test surface? What variable do we (or the text) usually use to indicate the test point location? Which parts of that test surface have nonzero electric flux through them? What is the result of the electric field magnitude, in terms of the test point variable you identified? Almost all of these are done in the text, class and/ lab tutorial, or you can find all of them by searching the web. source shape sphere, inside sphere, outside infinite cylinder, inside infinite cylinder, outside infinite plate test surface shape test point at nonzero flux through... E is
Transcribed Image Text:We have said that Gauss's law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. a) Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss's law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)? Why or why not? b) Can we use it for a uniformly charged ring? a uniformly charged cube? Why or why not? c) Summarize the key features for each of the possible distributions when the charge density is uniform throughout the sphere, cylinder or plate by filling out the table below answering the following questions: What is the shape of the test surface? What variable do we (or the text) usually use to indicate the test point location? Which parts of that test surface have nonzero electric flux through them? What is the result of the electric field magnitude, in terms of the test point variable you identified? Almost all of these are done in the text, class and/ lab tutorial, or you can find all of them by searching the web. source shape sphere, inside sphere, outside infinite cylinder, inside infinite cylinder, outside infinite plate test surface shape test point at nonzero flux through... E is
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for part c can you explain how you got each of the /E/ (last column)?

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