Consider a small sphere (an actual sphere, not a Gaussian surface) of radius R = 0.1 m that is charged throughout its interior, but not uniformly so. The charge density is p = Br , where r is the distance from the center, and B = 10ʻ C/m* is a constant. Of course, for r greater than R, the charge density is zero. R= 0.1 m (a) What does the charge density converge to as you approach the center of the sphere? Does it increase or decrease as we move toward the surface? Explain. (b) What does E converge to as you approach the center of the sphere? How do you know? How does this compare to the E of a point charge? [Hint: Consider the symmetry of the problem.]

Consider a small sphere (an actual sphere, not a Gaussian surface) of radius R = 0.1 m that is charged throughout its interior, but not uniformly so. The charge density is p = Br , where r is the distance from the center, and B = 10ʻ C/m* is a constant. Of course, for r greater than R, the charge density is zero. R= 0.1 m (a) What does the charge density converge to as you approach the center of the sphere? Does it increase or decrease as we move toward the surface? Explain. (b) What does E converge to as you approach the center of the sphere? How do you know? How does this compare to the E of a point charge? [Hint: Consider the symmetry of the problem.]

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 61P: An uncharged spherical conductor S of radius R has two spherical cavities A and B of radii a and b,...

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