The_Cambridge_Handbook_of_Physics_Formulas

144 Electromagnetism
Paramagnetism and diamagnetism
Diamagnetic
moment of an atom
Intrinsic electron
magnetic moment a
m = − e2
6m e
Z〈r 2 〉B (7.108)
m ≃− e
2m e
gJ (7.109)
m magnetic moment
〈r 2 〉 mean squared orbital radius
(of all electrons)
Z atomic number
B magnetic flux density
m e electron mass
−e electronic charge
J
g
total angular momentum
Landé g-factor (=2 for spin,
=1 for orbital momentum)
Langevin function
L(x)=cothx− 1 (7.110)
x
≃ x/3 (x ∼ < 1) (7.111)
L(x)
Langevin function
Classical gas
paramagnetism
(|J |≫¯h)
〈M〉 = nm 0 L
Curie’s law χ H = µ 0nm 2 0
3kT
( )
m0 B
kT
(7.112)
(7.113)
〈M〉
m 0
n
T
k
χ H
apparent magnetisation
magnitude of magnetic dipole
moment
dipole number density
temperature
Boltzmann constant
magnetic susceptibility
Curie–Weiss law χ H = µ 0nm 2 0
3k(T −T c )
a See also page 100.
(7.114)
µ 0 permeability of free space
T c Curie temperature
Boundary conditions for E, D, B, and H a
Parallel
component of the
electric field
Perpendicular
component of the
magnetic flux
density
E ‖ continuous (7.115) ‖ component parallel to
interface
B ⊥ continuous (7.116)
Electric
displacement b ŝ·(D 2 −D 1 )=σ (7.117)
Magnetic field
strength c ŝ×(H 2 −H 1 )=j s (7.118)
a At the plane surface between two uniform media.
b If σ =0, then D ⊥ is continuous.
c If j s = 0 then H ‖ is continuous.
⊥
D 1,2
ŝ
σ
H 1,2
j s
component
perpendicular to
interface
electrical displacements
in media 1 & 2
unit normal to surface,
directed 1 → 2
surface density of free
charge
magnetic field strengths
in media 1 & 2
surface current per unit
width
2
1
✻ŝ