 Solution

The Poynting vector is the local electromagnetic energy flux density:Here $\mathbf{E}$ is the electric field and $\mathbf{H}$ the magnetic field intensity. For an oriented area element $d\mathbf{S}$, $\mathbf{N}\cdot d\mathbf{S}$ is the electromagnetic power crossing that element in its positive normal direction. Thus ${\int }_S\mathbf{N}\cdot d\mathbf{S}$ is outward power through a closed surface, in watts. The Poynting vector has units $\mathrm{W}{\mathrm{m}}^{-2}$, and its direction describes local electromagnetic energy transport.