For the electric field results E x ′ = F 0 ′ 1 ′ = Λ Λ 0 μ μ Λ Λ 1 ν ν F μ μ ν ν = Λ Λ 0 1 Λ Λ 1 0 F 10 + Λ Λ 0 0 Λ Λ 1 1 F 01 = ( − − γ γ β β ) ( − − γ γ β β ) ( − − E x ) + γ γ γ γ E x = − − γ γ 2 β β 2 ( E x ) + γ γ 2 E x = E x ( 1 − − β β 2 ) γ γ 2 = E x , E y ′ = F 0 ′ 2 ′ = Λ Λ 0 μ μ Λ Λ 2 ν ν F μ μ ν ν = Λ Λ 0 μ μ Λ Λ 2 2 F μ μ 2 = Λ Λ 0 0 Λ Λ 2 2 F 02 + Λ Λ 0 1 Λ Λ 2 2 F 12 = γ γ × × 1 × × E y + ( − − β β γ γ ) × × 1 × × B z = γ γ E y − − β β γ γ B z = γ γ ( E + β β × × B ) y E z ′ = F 0 ′ 3 ′ = Λ Λ 0 μ μ Λ Λ 3 ν ν F μ μ ν ν = Λ Λ 0 μ μ Λ Λ 3 3 F μ μ 3 = Λ Λ 0 0 Λ Λ 3 3 F 03 + Λ Λ 0 1 Λ Λ 3 3 F 13 = γ γ × × 1 × × E z − − β β γ γ × × 1 × × ( − − B y ) = γ γ E z + β β γ γ B y = γ γ ( E + β β × × B ) z .