Subtracting the two last equations by members we get ∫ ∫ V [ J 1 ⋅ ⋅ E 2 − − E 1 ⋅ ⋅ J 2 ] d ⁡ ⁡ V = ∮ ∮ S [ E 1 × × H 2 − − E 2 × × H 1 ] ⋅ ⋅ d S . and equivalently in differential form J 1 ⋅ ⋅ E 2 − − E 1 ⋅ ⋅ J 2 = ∇ ∇ ⋅ ⋅ [ E 1 × × H 2 − − E 2 × × H 1 ] Q.E.D.