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FORMULA CONVERSION8

Here a = 102cmm_1, (3 = 107erg J~\ e0 = 8.8542 x 10~12Fm_1, fi0 = 4ttX 10~7 Hm_1, c = (e0Mo)~1/2 = 2.9979 X 108 m s_1, and h = 1.0546 X 10 —34 J s. To derive a dimensionally correct SI formula from one expressed in Gaussian units, substitute for each quantity according to Q = kQ, where k is the coefficient in the second column of the table corresponding to Q (overbars

denote variables expressed in Gaussian units). Thus, the formula do = K2/fhe2 for the Bohr radius becomes aao = (h(3)2 /[(m (3/a2) (e2 a (3/4tvco)] , or ao = eoh2/ivme2. To go from SI to natural units in which h = c = 1 (distinguished by a circumflex), use Q = k_1Q, where k is the coefficient corresponding to Q in the third column. Thus ao = AtvcoH2 /[(rhh/c)(e2 eohe)] = Aiz/rhe2. (In transforming from SI units, do not substitute for eo, Mo, or c.)

 Physical Quantity Gaussian Units to SI Natural Units to SI Capacitance Oi/47T6O eo"1 Charge (a(3/47re0)1/2 (eo he)-1'2 Charge density (/3/47m5e0)1/2 (eohc)~1/2 Current {a(3/47re0)1/2 (Mo/tic)1/2 Current density (/3/47m3e0)1/2 (vo/hc)1/2 Electric field (47T/3e0/a3)1/2 (eo/ftc)1/2 Electric potential (47T/3e0/«)1/2 (eo/Ac)1/2 Electric conductivity (47re0)"1 eo"1 Energy (3 (he)-1 Energy density (3/a3 (he)-1 Force (3 / a (he)-1 Frequency 1 c-1 Inductance 47T6o /OL Mo-1 Length a 1 Magnetic induction (47T/3/a3Mo)1/2 (Mo he)-1'2 Magnetic intensity (47T^0/3/a3)1/2 (Mo/AC)1/2 Mass (3/a2 c/H Momentum (3/a ft"1 Power (3 (he2)'1 Pressure (3/a3 (he)-1 Resistance 47T6o /OL (eo/no)1/2 Time 1 c Velocity a c-1

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