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3.4 Multipole Expansion

Dipole:. 3.4 Multipole Expansion. Approximate potential at large distance. Potential of a general charge distribution at large distance. Warning! The integral depends on the direction of r. Spherical harmonics:. solutions for 3D separation. Angular distribution at large distance.

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3.4 Multipole Expansion

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  1. Dipole: 3.4 Multipole Expansion Approximate potential at large distance

  2. Potential of a general charge distribution at large distance Warning! The integral depends on the direction of r.

  3. Spherical harmonics: solutions for 3D separation Angular distribution at large distance Addition theorem for Legendre polynomials:

  4. monopole dipole dipole moment The monopole and Dipole Terms

  5. physical dipole “pure” dipole is the limit Dipole moments are vectors and add accordingly. A quadrupole has no dipole moment.

  6. In general, multipole moments depend on the choice of the coordinate system. Has a dipole moment. If Q=0 the dipole moment does not depend on the coordinate system.

  7. The electric field of a dipole along the z-axis.

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