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Transcript
Chapter 11: Magnetic Multipoles For a spatially localized current density j(r), we may write B(r) = ∇ × A(r) where A(r) = μ0 4π ∫ j(r’) | r−r’ | d3r’ Expand in powers of r’/r with r > r’. This will give the asymptotic potential for r >> the size of the current carrying object. which is the multipole expansion for the vector potential. The magnetic monopole ( l = 0 ). The term with l = 0 is zero. Proof. The magnetic dipole ( l = 1 ). So, asymptotically, the term with l = 1 is dominant (unless it happens to be 0). The magnetic quadrupole term If the dipole moment is 0, then the dominant asymptotic field is the quadrupole field (unless it happens to be 0).
