(a) An insulating sphere with radius a has a uniform charge density p. The sphere is not centered at the origin but at i = b. Show that the electric field inside the sphere is given by E = p(* – b)/3ɛ, . (b) An insulating sphere of radius R has a spherical hole of radius a R located within its volume and centered a distance b from the center Charge density p of the sphere, where a

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter25: Gauss’s Law
Section: Chapter Questions
Problem 45PQ: What is the magnitude of the electric field just above the middle of a large, flat, horizontal sheet...
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(a) An insulating sphere with radius a has a uniform charge density
p.
The sphere is not centered at the origin but at i = b. Show that
the electric field inside the sphere is given by E = p(* – b)/3ɛ, .
(b) An insulating sphere of radius R has a spherical hole of radius a
R
located within its volume and centered a distance b from the center
Charge density p
of the sphere, where a<b<R (a cross section of the sphere is shown
in Fig.). The solid part of the sphere has a uniform volume charge
density p. Find the magnitude and direction of the electric field E
inside the hole, and show that E is uniform over the entire hole. [Hint: Use the principle of
superposition and the result of part (a).]
Transcribed Image Text:(a) An insulating sphere with radius a has a uniform charge density p. The sphere is not centered at the origin but at i = b. Show that the electric field inside the sphere is given by E = p(* – b)/3ɛ, . (b) An insulating sphere of radius R has a spherical hole of radius a R located within its volume and centered a distance b from the center Charge density p of the sphere, where a<b<R (a cross section of the sphere is shown in Fig.). The solid part of the sphere has a uniform volume charge density p. Find the magnitude and direction of the electric field E inside the hole, and show that E is uniform over the entire hole. [Hint: Use the principle of superposition and the result of part (a).]
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