Differentiate between monopole, dipole, quadrupole and octapole

Physics

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Here's a differentiation between monopole, dipole, quadrupole, and octapole:

  • A monopole is the simplest charge distribution, consisting of a single net charge (e.g., a point charge). Its field is the strongest and falls off slowest with distance, typically as 1/r21/r^2 for the electric field.
  • A dipole consists of two equal and opposite charges separated by a small distance. It has no net charge, and its field falls off faster than a monopole's, typically as 1/r31/r^3.
  • A quadrupole consists of two dipoles arranged such that their dipole moments cancel out, resulting in no net charge and no net dipole moment. Its field falls off even faster, typically as 1/r41/r^4. An example is four alternating charges arranged in a square.
  • An octapole is a higher-order multipole, consisting of two quadrupoles arranged to cancel out their quadrupole moments. It has no net charge, no net dipole moment, and no net quadrupole moment, with its field falling off as 1/r51/r^5.
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