Noting that the evolution of Josephson phase is φ φ ˙ ˙ = ϕ ϕ ˙ ˙ B − − ϕ ϕ ˙ ˙ A and the time derivative of charge carrier density n ˙ ˙ A is proportional to current I , when n A ≈ ≈ n B , the above solution yields the Josephson equations :