Answered: When an uncharged conducting sphere of…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 45PQ: The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r...

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When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field = E₀ , the resulting electric potential is V (x,y,z) = V₀ for the points inside the sphere and

V (x,y,z) = V₀ − E₀z +

E₀a³z

(x² + y² + z²)^3/2

for points outside the sphere, where V₀ is the (constant) electric potential on the conductor.

Use this equation to determine the x, y, and z components of the resulting electric field in the following regions. (Use the following as necessary: x, y, z, a, and E₀.)

(a) inside the sphere

(b) outside the sphere

Note: I already solved part a. I need help with part b. Look at the image for the full problem.

When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, k, the resulting electric potential is
0.
(x,y,z) = V. for the points inside the sphere and
V (x,y,z) = Vo
Eoz +
Ega z
(x2 + y? + z?)3/2
for points outside the sphere, where V, is the (constant) electric potential on the conductor.
Use this equation to determine the x, y, and z components of the resulting electric field in the following regions. (Use the following as necessary: x, y, z, a, and E.)
(a) inside the sphere
E = 0
Ey
E, = 0
(b) outside the sphere
Ex =0
Ey =
E =
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