I [A] =1 C/s 電流 1 A MKS 単位系について 2 D [C/ m ] 電束密度（電界） D= [ F / m ][ V / m ] 基本単位・距離・質量・時間 m kg s (メートル) (キロ・グラム) (秒、セカンド) ・電流 A (アンペア) 1 C/m = 1 s⋅A / m 2 力 V [V ] φ [ V ]（スカラー・ポテンシャル） 2 a [m/s ] E [V/m] = − grad φ F[N] 1 N = 1 J/m = 1 kg ⋅ m/s div ⋅ grad φ = ∇ 2φ = ∆φ = − 2 ∵ F = ma 1 V = 1 J/C W [ J ] = q [C] エネルギー W[J] 1J = 1 N⋅m ∵ W = Fs (仕事量=力×距離) kg ⋅ m 2 =1 s2 ⋅ C ∵ W = IVt (電力量=電流×電圧×時間) 1 ∵ W = mv 2 2 1 kg ⋅ m / s = 1 N ⋅s θ [ rad ] or [ deg ] 2π = 180 ※ 一般に角度の単位 rad はつけない角運動量 l [ J ⋅s ] 2 2 P= 1 C/m 2 =1 s⋅A m2 ∑p i V （電束密度と同じ単位） ――――――――――――――――――――――― 磁極（磁荷） qm [ Wb ] 1 Wb = 1 V ⋅ s ∵ Faraday’s Law: d (B ⋅ S ) [ Wb / s ] dt dB or rot E = − dt φV [ V ] = − = 1 J ⋅s = 1 Wb ⋅ C (磁極電極積) ――――――――――――――――――――――― p=qd P [ C/m ] l = mvr 1 kg ⋅ m / s kg ⋅ m 2 =1 s3 ⋅ A = 1 m ⋅s ⋅ A p = mv ∵ p = F ⋅∆t 角度 1 C⋅m 電気分極 p [ kg ⋅ m / s ] 運動量 φ [V] p [C⋅m ] 電気モーメント 2 ρ ε0 = 1 Wb/s = 1 V⋅ C = 1 Wb ⋅ A = 1 V⋅ A⋅ s 2 ∵ F [N] = q [C] E [ V / m ] kg ⋅ m =1 3 s ⋅A kg ⋅ m =1 2 s ⋅C 電位（電圧） = 1 kg⋅ m /s ρ [ C/m3 ] 電場 E [V/m] 1 V/m = 1 N/C v [m/s] 加速度 2 Gauss’s Law: div D = ――――――――――――――――――――――― 速度 ε0 E = 1 H⋅A ∵ Lentz’s Law: 電極（電荷） q [C] 1C = 1 A ⋅s = 1 F⋅V φV [ V ] = − L [ H ] ∵ Q[ C ] = C[ F ] V[ V ] dI [A/s] dt kg ⋅ m 2 s2 ⋅ A =1 B [ Wb / m ] B= = 1 s⋅V / m 2 S [m 2 ] C = ε0 d [m] 3 Gauss’s Law: div B = 0 [ Wb/m ] 1 F = 1 C/V ∵ Q [C ] = C [F] V [V ] 2 =1 H [A/m] Ampère’s Law: rot H = i 直線電流周りの磁場 H = I [A] 2π r [m] 1 J/A W [ J ] = qm[ Wb ] =1 H −1 ⋅ s2 dI [A/s] dt φV [ V ] = − L [ H ] φm [ A ] （磁気ポテンシャル） = 2 インダクタンス L[H] 1 H = 1 V ⋅s / A ∵ Lentz’s Law: = 1 Wb / A H [A/m] = − grad φm 1A s ⋅A kg ⋅ m 2 4 注意： [ Wb / m ] = [ T ] tesla 磁位 V ――――――――――――――――――――――― 電気容量 C[F] kg =1 2 s ⋅A 磁場 i B = µ 0 H + I = µ 0 ( H + M ) = µ 0 (1 + x) H µ0 H [ H / m ][ A / m ] 1 Wb / m ∑m M= 2 磁束密度（磁界） 2 M [ A/m ] 磁気分極（磁化）：磁場形式 =1 φm [ A ] kg ⋅ m s2 ⋅ A2 =1 F −1 2 A [ H ⋅ A / m ] （ベクトル・ポテンシャル） div ⋅ grad A = ∇ 2 A = ∆ A = − µ 0 i kg ⋅ m 1 H ⋅ A / m = 1 Wb / m = 1 2 s ⋅A B = rot A 2 rot B = rot rot A = grad div A − ∇ A = −∇ 2 A = µ 0 i 誘電率 µ [ Wb ⋅ m ] 1 Wb ⋅ m µ = qm d = 1 m ⋅s ⋅ V =1 1 F/m 磁気モーメント：磁場形式 µ = µo m [ Wb ⋅ m ] = [ H / m ][ A m ] 2 1 J/T 2 = 1 Am Zeeman’s Law : U = −m ⋅ B = − µ0 m ⋅ H = − µ ⋅ H 磁気分極（磁化） =1 2 =1 I [ Wb/m ] s⋅V kg =1 2 2 m s ⋅A 2 µ [H/m] B [ Wb / m ] = µ H [ A / m ] 2 = 1 Wb / A ⋅ m 2 = 1 kg ⋅ m kg ⋅ m =1 2 2 2 C sA ２本の直流電流間の引力光速との関係 F [ N /m] = ε 0 ⋅ µ0 = µ0 I1 I 2 2π d 1 2 2 [ s /m ] 2 C ――――――――――――――――――――――― 真空誘電率 permittivity of free space ε 0 = 107 / 4π C 2 m / H 2 I= 1 Wb/m s ⋅A kg ⋅ m3 4 =1 N/A m [J/T] ε E [V/m] 2 透磁率 S [m 2 ] d [m] ε = 1 C/ V⋅m D [ C/m ] = 1 H/m kg ⋅ m3 s2 ⋅ A ε [F/m ] C [F] = すなはち、rot H = i 磁気モーメント注意： [ H ][ F ] = [ s ] ∑µ i V （磁束密度と同じ単位）真空透磁率 permeability of free space µ 0 = 4π /107 H / m