The scalar product of the induction equation with 1 μ μ 0 B gives the rate of increase of the magnetic energy density, 1 2 μ μ 0 B 2 , on the left-hand side. The last term on the right-hand side is then 1 μ μ 0 B ⋅ ⋅ ( ∇ ∇ × × ( u × × B ) ) . Since the equation is volume-integrated, this term is equivalent up to a boundary term (and with the double use of the scalar triple product identity) to − − u ⋅ ⋅ ( 1 μ μ 0 ( ∇ ∇ × × B ) × × B ) = − − u ⋅ ⋅ ( J × × B ) (where one of Maxwell's equations was used). This is the local contribution to the magnetic energy due to fluid motion.