Space Physics Formulas:
Complement to Physics Handbook
Charge density and current density from particle species s:
ρ=X
s
qsns,j=X
s
qsnsvs
Galilean transformations:
E0=E+v×B,B0=B
Dipole magnetic field:
B(r, θ) = −B0R0
r32ˆr cos θ+ˆ
θsin θ
Dipole field lines:
r/ sin2θ= const.
Magnetic field energy density and pressure:
wB=pB=B2
2µ0
Equation of motion of neutral gas:
ρm
dv
dt =−∇p+ other forces
Equation of motion of gas of charged particle species s:
msns
dvs
dt =nsqs(E+vs×B)− ∇ps+ o.f.
MHD equation of motion:
ρm
dv
dt =j×B− ∇p+ o.f.=−∇ p+B2
2µ0+1
µ0
(B·∇)B+ o.f.
Equation of continuity:
∂n
∂t +∇ · (nv) = Q−L
Equation of state for ideal gas:
p=nKT
Dynamic pressure:
pdyn =1
2nmv2
Condition for ”frozen-in” magnetic field:
E+v×B= 0
Ohm’s law:
j=
σP−σH0
σHσP0
0 0 σk
Ex
Ey
Ek
=σPE⊥+σH
B×E⊥
B+σkEk
Conductivities:
σP=ne
Bωciνi
ω2
ci+ν2
i
+ωceνe
ω2
ce+ν2
e
σH=ne
Bω2
ci
ω2
ci+ν2
i
−ω2
ce
ω2
ce+ν2
e
σk=ne21
miνi+1
meνe
1
