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Question 2: Conducting sphere in a uniform Electric Field by method of images. We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. << = Q/4 TEO (2+R2+2rR cos 0) 1/2 Q/4 πTEO (2 R2 2rR cos 0)1/2 - aQ/4πEO a4 2a²r aQ/4πEO 1/2 Rr² + + R2 R a4 2a²r cos R2+ - R2 R cos 8 $ = Απερ 1414 - 20 cos 0 + 2Q a³ r R² +20% cos 0] + +... (2.12) 1/2 (2.13) where the omitted terms vanish in the limit R. In that limit 2Q/4TER² becomes the applied uniform field, so that the potential is - Eo(r-2) cos 0 $ = − ] (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.

Question 2: Conducting sphere in a uniform Electric Field by method of images. We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. << = Q/4 TEO (2+R2+2rR cos 0) 1/2 Q/4 πTEO (2 R2 2rR cos 0)1/2 - aQ/4πEO a4 2a²r aQ/4πEO 1/2 Rr² + + R2 R a4 2a²r cos R2+ - R2 R cos 8 $ = Απερ 1414 - 20 cos 0 + 2Q a³ r R² +20% cos 0] + +... (2.12) 1/2 (2.13) where the omitted terms vanish in the limit R. In that limit 2Q/4TER² becomes the applied uniform field, so that the potential is - Eo(r-2) cos 0 $ = − ] (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question 2: Conducting sphere in a uniform Electric Field by method of images. We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. << = Q/4 TEO (2+R2+2rR cos 0) 1/2 Q/4 πTEO (2 R2 2rR cos 0)1/2 - aQ/4πEO a4 2a²r aQ/4πEO 1/2 Rr² + + R2 R a4 2a²r cos R2+ - R2 R cos 8 $ = Απερ 1414 - 20 cos 0 + 2Q a³ r R² +20% cos 0] + +... (2.12) 1/2 (2.13) where the omitted terms vanish in the limit R. In that limit 2Q/4TER² becomes the applied uniform field, so that the potential is - Eo(r-2) cos 0 $ = − ] (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.
Transcribed Image Text:Question 2: Conducting sphere in a uniform Electric Field by method of images. We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. << = Q/4 TEO (2+R2+2rR cos 0) 1/2 Q/4 πTEO (2 R2 2rR cos 0)1/2 - aQ/4πEO a4 2a²r aQ/4πEO 1/2 Rr² + + R2 R a4 2a²r cos R2+ - R2 R cos 8 $ = Απερ 1414 - 20 cos 0 + 2Q a³ r R² +20% cos 0] + +... (2.12) 1/2 (2.13) where the omitted terms vanish in the limit R. In that limit 2Q/4TER² becomes the applied uniform field, so that the potential is - Eo(r-2) cos 0 $ = − ] (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.
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