2 Old and nice grammar..
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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
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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.