Consider a spherical surface of radius R centered on the origin and carrying a uni- form charge density o. Find the electric field a distance z along the z-axis, using direct integration (i.e., not Gauss's Law). Treat the case z < R (inside) as well as z > R (outside). Express your answers in terms of the total charge q on the sphere. [Hint: Use the law of cosines to write w in terms of R and 0. Be sure to take the positive square root: √(R – z)² is R – z if R > z, and is z − R if R < z.] Now repeat the calculation using Gauss's Law, and show that you get the same answer (although this time much more easily).

Consider a spherical surface of radius R centered on the origin and carrying a uni- form charge density o. Find the electric field a distance z along the z-axis, using direct integration (i.e., not Gauss's Law). Treat the case z < R (inside) as well as z > R (outside). Express your answers in terms of the total charge q on the sphere. [Hint: Use the law of cosines to write w in terms of R and 0. Be sure to take the positive square root: √(R – z)² is R – z if R > z, and is z − R if R < z.] Now repeat the calculation using Gauss's Law, and show that you get the same answer (although this time much more easily).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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