2 Old and nice grammar.. edited May 12 '15 at 21:53 Physicist137 2,49511 gold badge99 silver badges2323 bronze badges Of course it is consistent. As commented, this is exactly the equation for a conducting mediamedium. $$\nabla\times\mathbf B = \mu\sigma\mathbf E + \mu\epsilon\frac{\partial\mathbf E}{\partial t}$$ For instance, this is exactly the equation used to derive the wave equation in a conducting mediamedium with no charge density: $$\nabla^2\mathbf E = \mu\epsilon\frac{\partial^2\mathbf E}{\partial t^2} + \sigma\mu\frac{\partial\mathbf E}{\partial t}$$ Which exactly gives a term for the attenuation effect of the wave due to the conductivity of the mediamedium. Of course it is consistent. As commented, this is exactly the equation for a conducting media. $$\nabla\times\mathbf B = \mu\sigma\mathbf E + \mu\epsilon\frac{\partial\mathbf E}{\partial t}$$ For instance, this is exactly the equation used to derive the wave equation in a conducting media with no charge density: $$\nabla^2\mathbf E = \mu\epsilon\frac{\partial^2\mathbf E}{\partial t^2} + \sigma\mu\frac{\partial\mathbf E}{\partial t}$$ Which exactly gives a term for the attenuation effect of the wave due to the conductivity of the media. Of course it is consistent. As commented, this is exactly the equation for a conducting medium. $$\nabla\times\mathbf B = \mu\sigma\mathbf E + \mu\epsilon\frac{\partial\mathbf E}{\partial t}$$ For instance, this is exactly the equation used to derive the wave equation in a conducting medium with no charge density: $$\nabla^2\mathbf E = \mu\epsilon\frac{\partial^2\mathbf E}{\partial t^2} + \sigma\mu\frac{\partial\mathbf E}{\partial t}$$ Which exactly gives a term for the attenuation effect of the wave due to the conductivity of the medium. 1 answered May 12 '15 at 12:58 Physicist137 2,49511 gold badge99 silver badges2323 bronze badges Of course it is consistent. As commented, this is exactly the equation for a conducting media. $$\nabla\times\mathbf B = \mu\sigma\mathbf E + \mu\epsilon\frac{\partial\mathbf E}{\partial t}$$ For instance, this is exactly the equation used to derive the wave equation in a conducting media with no charge density: $$\nabla^2\mathbf E = \mu\epsilon\frac{\partial^2\mathbf E}{\partial t^2} + \sigma\mu\frac{\partial\mathbf E}{\partial t}$$ Which exactly gives a term for the attenuation effect of the wave due to the conductivity of the media.