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1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+

1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+

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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1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+
Transcribed Image Text:1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+
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