Consider a small sphere (an actual sphere, not a Gaussian surface) of radius = 0.1 m R that is charged throughout its interior, but not uniformly so. The charge density is, where is the distance from the center, and = 10-4 C/m4 is a constant. Of course, r B for greater than the charge density is zero. r R, 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. 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.] Apply Law to find an expression for when is less than [Hint: the E r R. Gauss’ volume of a thin spherical shell of radius and thickness is .] r dr What is at = 0.05 m? [Your answer should be in N/C.] E r
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, where r is the distance from the center, and B = 10-4 C/m4 is a constant. Of course, for r greater than R, the charge density is zero. 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. 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.] Apply Gauss’ Law to find an expression for E when r is less than R. [Hint: the volume of a thin spherical shell of radius r and thickness dr is .] What is E at r = 0.05 m? [Your answer should be in N/C.]