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Multipole expansion
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Expand potential into monopole, dipole and quadrupole terms.
At large distance the potential of any charge distribution expands into monopole (1/r), dipole (1/r²), quadrupole (1/r³) terms. The first nonzero term dominates.
Neutral molecules show dipole fields.
Each term falls faster than the one before.
In more detail
A multipole expansion represents the potential of a charge distribution as a series of terms: monopole, dipole, quadrupole and so on. At large distances, the lowest non-zero term dominates.
Real-world uses
- Chemists model molecular interactions using multipole expansions.
- Geophysicists use multipole models for Earth's gravitational field.
- Chemists use multipole expansions to approximate the field of a molecule at large distances.
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Frequently asked questions
What is the monopole term?
The total charge, which dominates at large distances if non-zero.
Why is the dipole important for molecules?
Because many molecules have a net dipole moment even when their net charge is zero.
When do higher multipoles matter?
They matter close to the charge distribution, while at large distance the monopole and dipole terms usually dominate.
Related topics in Electrostatics
Cathode ray tube · Method of images · Poisson's and Laplace's equations · Boundary conditions at interfaces · Electrostatic energy of a sphere · Earnshaw's theorem