by Nikolai Shokhirev

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Dimensions and units

Dimensions are very useful for qualitative checks of equations. 

  Quantity   Dimensions   Units
  Kinetic energy      kg m 2 s -2 = N m
  = J (joule)
  Zeeman interaction      kg m 2 s -2 = N m = J (joule)
  Coulomb interaction energy      kg m 2 s -2 = N m = J (joule)
 Permittivity of vacuum      A s V -1 m -1
  = F m -1
  = A 2 s 4 kg -1 m -3
  Permeability of vacuum      H m -1 = T m A -1
  = Wb A -1 m -1
  = V s A -1 m -1
  Thermal energy, Amount of heat      kg m 2 s -2 = N m = J (joule)
     
  Angular momentum       kg m 2 s -1 = J s
  Magnetic moment       A m2  
  Magnetic field B
(Magnetic flux density)
     Wb/m2 = kg·s-2·A-1 = T (tesla)
  gyromagnetic ratio       A s kg -1 = C kg -1
  = s -1 T -1
  Gravitational constant       m 3 kg -1 s -2
  = N m 2 kg -2

 

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