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MMLU-Pro / 11940 / Anelectrethas a permanent electric dipole moment in the absenceof free charges.…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Anelectrethas a permanent electric dipole moment in the absenceof free charges. Given anelectretsphere of radius R, with electricpolarisationvectorP= r̂ Po r. Determine the bound charge density \rho', electric displacementvectorD, and the electric fieldEas functions ofr.

category

engineering

options

  1. ρ' = P_0 / 3, D = ε_0r̂P_0, E = r̂(3P_0 / ε_0) for r < R and E(r > R) = r̂(P_0 / ε_0)
  2. ρ' = -P_0 / r^2, D = ε_0r̂P_0r, E = -r̂(P_0 / ε_0r^2) for r < R and E(r > R) = -r̂(P_0 / ε_0R^2)
  3. ρ' = 2P_0, D = ε_0r̂P_0r, E = r̂(2P_0r / ε_0) for r < R and E(r > R) = r̂(2P_0R / ε_0)
  4. ho' = - 3P_0, D = 0, E = - r̂(P_0r / \epsilon_0) for r > R and E(r < R) = 0
  5. ho' = - 3P_0, D = 0, E = - r̂(P_0r / \epsilon_0) for r < R and E(r > R) = 0
  6. ρ' = 0, D = ε_0r̂P_0, E = r̂(P_0r^2 / ε_0) for r < R and E(r > R) = 0
  7. ρ' = P_0r, D = ε_0r̂(P_0r^2), E = r̂(P_0 / ε_0) for r < R and E(r > R) = r̂(P_0R / ε_0)
  8. ρ' = -2P_0/r, D = ε_0r̂(P_0r), E = -r̂(2P_0 / ε_0r) for r < R and E(r > R) = -r̂(2P_0 / ε_0R)
  9. ho' = 3P_0, D = 1, E = r̂(P_0r / \epsilon_0) for r < R and E(r > R) = 0
  10. ho' = - 3P_0, D = 1, E = - r̂(P_0r / \epsilon_0) for r < R and E(r > R) = 1

src

stemez-Electromagnetics

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Source and history

upstream_id / Original problem ID
11940
task_id
42dfd522-3679-5e32-abaa-3ee474c338d4
task_key
default--test--11940
task_revision_id
1
config / split
default / test

Official source

initial import