Space Physics Formulas: Complement to Physics Handbook, Exercises of Physics

Download Space Physics Formulas: Complement to Physics Handbook and more Exercises Physics in PDF only on Docsity! Space Physics Formulas: Complement to Physics Handbook Charge density and current density from particle species s: ρ = ∑ s qsns, j = ∑ s qsnsvs Galilean transformations: E′ = E + v ×B, B′ = B Dipole magnetic field: B(r, θ) = −B0 ( R0 r )3 ( 2r̂ cos θ + θ̂ sin θ ) Dipole field lines: r/ sin2 θ = 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 2 nmv2 Condition for ”frozen-in” magnetic field: E + v ×B = 0 Ohm’s law: j =  σP −σH 0 σH σP 0 0 0 σ‖  Ex Ey E‖  = σPE⊥ + σH B×E⊥ B + σ‖E‖ Conductivities: σP = ne B ( ωciνi ω2 ci +ν2 i + ωceνe ω2 ce+ν 2 e ) σH = ne B ( ω2 ci ω2 ci +ν2 i − ω2 ce ω2 ce+ν 2 e ) σ‖ = ne2 ( 1 miνi + 1 meνe ) 1