Question

A spherical conductor, of radius a, carries a charge Q. It is surrounded by linear dielectric material of electric susceptibility ?E, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by D = { 0, r < a; Q/(4?r^2) r?, r > a E = { Q/(4??r^2) r?, a < r < b; Q/(4??0r^2) r?, r > b respectively. Find the energy of this charge configuration.

Name: A spherical conductor, of radius a, carries a charge Q. It is surrounded by linear dielectric material of electric susceptibility ?E, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by D = 0, r a E = Q/(4??r^2) r?, a b respectively. Find the energy of this charge configuration.
Uploaded: 2022-04-06T07:49:34-08:00
Duration: 1 min 41 s
Channel: Sri K
Description: A spherical conductor, of radius a, carries a charge Q. It is surrounded by linear dielectric material of electric susceptibility ?E, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by D = 0, r a E = Q/(4??r^2) r?, a b respectively. Find the energy of this charge configuration.

          A spherical conductor, of radius a, carries a charge Q. It is surrounded by linear dielectric material of electric susceptibility ?E, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by

D = { 0, r < a; Q/(4?r^2) r?, r > a

E = { Q/(4??r^2) r?, a < r < b; Q/(4??0r^2) r?, r > b

respectively. Find the energy of this charge configuration.

A spherical conductor, of radius a, carries a charge Q. It is surrounded by linear dielectric material of electric susceptibility ?E, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by

D = 0, r < a; Q/(4?r^2) r?, r > a

E = Q/(4??r^2) r?, a < r < b; Q/(4??0r^2) r?, r > b

respectively. Find the energy of this charge configuration.

Added by David T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

04/06/2022

Step 1

The energy density of an electric field is given by u = 1/2 * ε * E^2. For r < a, the energy density is u = 1/2 * ε0 * (GQ/(4πε0r^2))^2 = G^2Q^2/(32π^2ε0r^4). For a < r < b, the energy density is u = 1/2 * ε0 * ((GQ/(4πε0r^2) + GXE/ε0)^2) = G^2Q^2/(32π^2ε0r^4) Show more…

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A spherical conductor of radius a carries charge Q. It is surrounded by linear dielectric material of electric susceptibility XE, out to radius b. The electric displacement field, D, and electric field, E, of this configuration are given by: Find the energy of this charge configuration.

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