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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).