rpp2010-rev-electromag-relations

rpp2010-rev-electromag-relations - 7 Electromagnetic...

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7. Electromagnetic relations 1 7. ELECTROMAGNETIC RELATIONS Revised September 2005 by H.G. Spieler (LBNL). Quantity Gaussian CGS SI Conversion factors: Charge: 2 . 997 924 58 × 10 9 esu = 1 C = 1 A s Potential: (1 / 299 . 792 458) statvolt (ergs/esu) = 1 V = 1 J C 1 Magnetic field: 10 4 gauss = 10 4 dyne/esu = 1 T = 1 N A 1 m 1 F = q ( E + v c × B ) F = q ( E + v × B ) . D = 4 πρ . D = ρ × H 1 c D ∂t = 4 π c J × H D ∂t = J . B = 0 . B = 0 × E + 1 c B ∂t = 0 × E + B ∂t = 0 Constitutive relations: D = E + 4 π P , H = B 4 π M D = 0 E + P , H = B 0 M Linear media: D = E , H = B D = E , H = B 1 0 = 8 . 854 187 . . . × 10 12 F m 1 1 μ 0 = 4 π × 10 7 N A 2 E = V 1 c A ∂t E = V A ∂t B = × A B = × A V = charges q i r i = ρ ( r ) | r r | d 3 x V = 1 4 π 0 charges q i r i = 1 4 π 0 ρ ( r ) | r r | d 3 x A = 1 c I d | r r | = 1 c J ( r ) | r r | d 3 x A = μ 0 4 π I d | r r | = μ 0 4 π J ( r ) | r r | d 3 x E = E E = E E = γ ( E + 1 c v × B ) E = γ ( E + v × B ) B = B B = B B = γ ( B 1 c v × E ) B = γ ( B 1 c 2 v × E ) 1 4 π 0 = c 2 × 10 7 N A 2 = 8 . 987 55 . . . × 10 9 m F 1 ; μ 0 4 π = 10 7 N A 2 ; c = 1 μ 0 0 = 2 . 997 924 58 × 10 8 m s 1
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2 7. Electromagnetic relations 7.1. Impedances (SI units) ρ = resistivity at room temperature in 10 8 Ω m:
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