where the second term is a surface integral over the boundary surface ∂ ∂ V of the closed system. The dot product in the integrand of the first term is zero because ∇ ∇ × × A = B is orthogonal to ∂ ∂ A / ∂ ∂ t . The second term also vanishes because motions inside the closed system cannot affect the vector potential outside, so that at the boundary surface ∂ ∂ A / ∂ ∂ t = 0 since the magnetic vector potential is a continuous function. Therefore,