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(a) What is the charge density at the center? Does it increase or decrease as we move toward the surface? Justify your answer. (b) What is E at the center? How do you know? How does this compare to the E of a point charge? Justify your answer.

(a) What is the charge density at the center? Does it increase or decrease as we move toward the surface? Justify your answer. (b) What is E at the center? How do you know? How does this compare to the E of a point charge? Justify your answer.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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Need help please Equation is. ∫E•dA (integrated over a closed surface) = q enclosed/∈o
2. If possible, pick a closed "Gaussian" surface or surfaces appropriate for the geometry of the charge distribution at hand such that the electric field can be determined. Here's another problem requiring Gauss' Law, but this time you will have to do a bit of integration. Consider a small sphere (an actual sphere, not a Gaussian surface) of radius 0.1 m that is charged throughout its interior, but not uniformly so. The charge density (in C/m³) is o=Br, where r is the distance from the center, and B-10-C/m² is a constant. Of course, for r greater than 0.1 m, the charge density is zero. (a) What is the charge density at the center? Does it increase or decrease as we move toward the surface? Justify your answer. (b) What is E at the center? How do you know? How does this compare to the E of a point charge? Justify your answer. (c) Apply Gauss' Law to find E at r=0.05 m. Your answer should be in N/C Hint: the volume of a thin spherical shell is dv=4nr dr. You can find E(r) for r inside the sphere and then evaluate at r=0.05 m. Also, use value for so (d) Make a graph of E versus r, using proper scale and units For appropriate cases of charge distributions explain (combinations of equations liberally sprinkled with words of explanation are appropriate here) how Gauss's law can be applied to find the electric field in all regions of space. Then demonstrate the technique by finding mathematical expressions for E in those regions.
Transcribed Image Text:2. If possible, pick a closed "Gaussian" surface or surfaces appropriate for the geometry of the charge distribution at hand such that the electric field can be determined. Here's another problem requiring Gauss' Law, but this time you will have to do a bit of integration. Consider a small sphere (an actual sphere, not a Gaussian surface) of radius 0.1 m that is charged throughout its interior, but not uniformly so. The charge density (in C/m³) is o=Br, where r is the distance from the center, and B-10-C/m² is a constant. Of course, for r greater than 0.1 m, the charge density is zero. (a) What is the charge density at the center? Does it increase or decrease as we move toward the surface? Justify your answer. (b) What is E at the center? How do you know? How does this compare to the E of a point charge? Justify your answer. (c) Apply Gauss' Law to find E at r=0.05 m. Your answer should be in N/C Hint: the volume of a thin spherical shell is dv=4nr dr. You can find E(r) for r inside the sphere and then evaluate at r=0.05 m. Also, use value for so (d) Make a graph of E versus r, using proper scale and units For appropriate cases of charge distributions explain (combinations of equations liberally sprinkled with words of explanation are appropriate here) how Gauss's law can be applied to find the electric field in all regions of space. Then demonstrate the technique by finding mathematical expressions for E in those regions.
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