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Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2rr dr. (b) If the disk carries pos- itive surface charge density ơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at any point on the disk axis, taken to be the x-axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude R -dr FIGURE 20.35 Problem 73 |x| Vx² + R². E = 2Tko( 1 Use the result uniformly charged flat sheet is 2īko, where o is the surface charge density. (This result is independent of distance from the sheet.) to show that the field of an infinite,

Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2rr dr. (b) If the disk carries pos- itive surface charge density ơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at any point on the disk axis, taken to be the x-axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude R -dr FIGURE 20.35 Problem 73 |x| Vx² + R². E = 2Tko( 1 Use the result uniformly charged flat sheet is 2īko, where o is the surface charge density. (This result is independent of distance from the sheet.) to show that the field of an infinite,

College Physics
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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Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2rr dr. (b) If the disk carries pos- itive surface charge density ơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at any point on the disk axis, taken to be the x-axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude R -dr FIGURE 20.35 Problem 73 |x| Vx² + R². E = 2Tko( 1 Use the result uniformly charged flat sheet is 2īko, where o is the surface charge density. (This result is independent of distance from the sheet.) to show that the field of an infinite,
Transcribed Image Text:Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2rr dr. (b) If the disk carries pos- itive surface charge density ơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the result of (b) along with the result of Example 20.6 to write the infinitesimal electric field dE of this ring at any point on the disk axis, taken to be the x-axis. (d) Integrate over all such rings to show that the net electric field on the axis has magnitude R -dr FIGURE 20.35 Problem 73 |x| Vx² + R². E = 2Tko( 1 Use the result uniformly charged flat sheet is 2īko, where o is the surface charge density. (This result is independent of distance from the sheet.) to show that the field of an infinite,
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