SI_Units_EM_Quantities

UIUC Physics 435 Electromagnetic Fields & Sources I Fall Semester, 2007 Professor Steven Errede SI Units of Kinematic and Electromagnetic Quantities Quantity Symbol Common Units Units Symbol SI Base Units Length A Meters, m m m Mass m Kilograms, kg kg kg Time t Seconds, sec or s s s Velocity v m/s m/s m/s Acceleration a m/s2 m/s2 m/s2 Force F = ma = dp/dt Newtons = kg-m/s2 N kg-m/s2 Momentum p = mv kg-m/s kg-m/s kg-m/s Angular Momentum L = r×p kg-m2/s = Joule-sec = N-m-s J-s = N-m-s kg-m2/s Pressure P = F/A Pascals, Pa = N/m2 Pa = N/m2 kg/m-s2 Energy, Work E, W Joules = N-m J = N-m kg-m2/s2 (Volume) Energy Density U = E/V Joules/m3 J/m3 kg/m-s2 Power P = dW/dt Watts = Joules/sec J/s kg-m2/s3 Electric Charge Q Coulombs, C C = A-s Ampere-sec Linear Elect. Charge Density λ = Q/L Coulombs/m C/m A-s/m Surface Elect. Charge Density σ = Q/A Coulombs/m2 C/m2 A-s/m2 Volume Elect. Charge Density ρ = Q/V Coulombs/m3 C/m3 A-s/m3 Electric Potential V Volts = N-m/C V = N-m/C kg-m2/A-s3 Electric Field E = F/Q = −∇V Volts/m = N/C V/m = N/C kg-m/A-s3 Electric Displacement D = εE Coulombs/m2 C/m2 A-s/m2 Electric Polarization P = εoχeE Coulombs/m2 C/m2 A-s/m2 Electric Flux ΦE = E•A = Q/εo Volt-m = N-m2/C V-m =N-m2/C kg-m3/A-s3 Electric Displacement Flux ΦD = D•A = Q Coulombs C = A-s A-s Capacitance C = Q/ V Farad = Coulomb/Volt F = C/V A2-s4/kg-m2 Electric Permittivity ε = εo(1+χe) Farads/m = C2/N-m2 F/m = C/V-m A2-s4/kg-m3 Electric Susceptibility χe =K e–1 = ε/εo–1 Dimensionless * * Electric Line Current I = J•A⊥ = K•A⊥ Amperes, Amps A = C/s A Elect. Surface Current Density K Amps/m A/m A/m Elect. Volume Current Density J = nq v Amps/m2 A/m2 A/m2 Magnetic Charge g m = “qv” Amp-m = C-m/s A-m A-m Magnetic Vector Potential A = “p/Q” Tesla-m = Wb/m = N/A T-m = N/A kg-m/A-s2 Magnetic Field B = ∇×A Teslas = Wb/m2 = N/A-m T = Wb/m2 kg/A-s2 Magnetic Displacement H = 1/μo B Amps/m A/m A/m Magnetization M = χmH Amps/m A/m A/m Magnetic Flux Φm = B•A = h/e Webers = Tesla-m2 = N-m/A Wb = T-m2 kg-m2/A-s2 Inductance L = Φm/I Henrys=Wb/A=T-m2/A=N-m/A2 H = N-m/A2 kg-m2/A2-s2 Magnetic Permeability μ = μo(1+χm) Henrys/m =T-m/A = N/A2 H/m = N/A2 kg-m/A2-s2 Magnetic Susceptibility χm =K m–1 = μ/μo–1 Dimensionless * * Resistance R = ρcA/A = V/I Ohms, Ω Ω =V/A kg-m2/A2-s3 Resistivity ρc = 1/σc Ohm-m, Ω-m Ω-m =V-m/A kg-m3/A2-s3 Conductance G = 1/R = σcA/A Siemens = Ω−1 = “Mhos” S = A/V A2-s3/kg-m2 Conductivity σc = 1/ρc Siemens/m = Ω−1/m = “Mhos”/m S/m = A/V-m A2-s3/kg-m3 Electric Charge e 1.602×10−19 Coulombs C C Magnetic Charge g 3.291×10−9 Ampere-meters A-m = C-m/s A-m Speed of Light (in vacuum) c =1/sqrt( εoμo) 2.998 ×108 meters/sec m/s m/s Elect. Permittivity Free Space εo 8.85 ×10−12 Farads/meter F/m = C2/N-m2 A2-s4/kg-m3 Magn. Permeability Free Space μo 4 π×10−7 Henrys/meter H/m = N/A2 kg-m/A2-s2 Planck’s Constant h 6.626×10−34 Joule-sec J-s = N-m-s kg-m2/s Boltzmann’s Constant kB 1.381×10−23 Joule/Kelvin J/K = N-m/K kg-m2/s2-K