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a) In lecture we solved the problem of the electric field from a spherical shell of radius R with uniform surface charge density o q/(4TTR2). Consider now the problem where this shell is of finite thickness d. That is, there is a uniform charge density p in a spherical shell of finite thickness from radius R to radius R+d, such that the total charge on this shell is q. Find the potential p(r) by solving Poisson's equation (there may be easier ways to do it, but do it this way!), then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping pd a constant. Compare your result with the case of the infinitesmally thin shell done in lecture. b) Consider an infinitesmally thin spherical shell of radius R with a total charge q uniformly distributed over its surface, and a concentric infinitesmally thin spherical shell of radius R+d with total charge -q uniformly distributed over its surface. Find the potential p(r) by solving Poisson's equation for this geometry, then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping qd constant. What do you find? This is the limit of an infinitesmally thin dipole layer.

a) In lecture we solved the problem of the electric field from a spherical shell of radius R with uniform surface charge density o q/(4TTR2). Consider now the problem where this shell is of finite thickness d. That is, there is a uniform charge density p in a spherical shell of finite thickness from radius R to radius R+d, such that the total charge on this shell is q. Find the potential p(r) by solving Poisson's equation (there may be easier ways to do it, but do it this way!), then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping pd a constant. Compare your result with the case of the infinitesmally thin shell done in lecture. b) Consider an infinitesmally thin spherical shell of radius R with a total charge q uniformly distributed over its surface, and a concentric infinitesmally thin spherical shell of radius R+d with total charge -q uniformly distributed over its surface. Find the potential p(r) by solving Poisson's equation for this geometry, then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping qd constant. What do you find? This is the limit of an infinitesmally thin dipole layer.

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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a) In lecture we solved the problem of the electric field from a spherical shell of radius R with uniform surface charge density o q/(4TTR2). Consider now the problem where this shell is of finite thickness d. That is, there is a uniform charge density p in a spherical shell of finite thickness from radius R to radius R+d, such that the total charge on this shell is q. Find the potential p(r) by solving Poisson's equation (there may be easier ways to do it, but do it this way!), then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping pd a constant. Compare your result with the case of the infinitesmally thin shell done in lecture. b) Consider an infinitesmally thin spherical shell of radius R with a total charge q uniformly distributed over its surface, and a concentric infinitesmally thin spherical shell of radius R+d with total charge -q uniformly distributed over its surface. Find the potential p(r) by solving Poisson's equation for this geometry, then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping qd constant. What do you find? This is the limit of an infinitesmally thin dipole layer.
Transcribed Image Text:a) In lecture we solved the problem of the electric field from a spherical shell of radius R with uniform surface charge density o q/(4TTR2). Consider now the problem where this shell is of finite thickness d. That is, there is a uniform charge density p in a spherical shell of finite thickness from radius R to radius R+d, such that the total charge on this shell is q. Find the potential p(r) by solving Poisson's equation (there may be easier ways to do it, but do it this way!), then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping pd a constant. Compare your result with the case of the infinitesmally thin shell done in lecture. b) Consider an infinitesmally thin spherical shell of radius R with a total charge q uniformly distributed over its surface, and a concentric infinitesmally thin spherical shell of radius R+d with total charge -q uniformly distributed over its surface. Find the potential p(r) by solving Poisson's equation for this geometry, then take the gradient to get E(r). Sketch p(r) and E(r) vs r. Now take the limit d-0 keeping qd constant. What do you find? This is the limit of an infinitesmally thin dipole layer.
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