In Ionospheric Dynamo Current equation

$j=\sigma(E+v\times B)$

where $j$ is the current density, $\sigma$ is the tensor conductivity, $v$ is the velocity of the tidal wind velocity (hence the velocity imparted to the ions), $B$ is the magnetic flux density of northward geomagnetic field and $E$ is the electric field.

My question is which electric field does $E$ actually represents? The electric field caused by the drag of ions against the magnetic field, or the electric field by the ions themselves?


In this approximation, the electric field is $\vec {E}=-\nabla \phi$ and $\nabla .\vec {j} =0$. Consequently $\nabla ^2\phi =\vec {B}.(\nabla \times \vec {v})$. Force acting on fluid volume unit is $\vec {f}=[\vec {j}\times\vec {B}]$. In the next approximation, ions and electrons are separated, it is necessary to take into account the contribution of the charges of ions and electrons in the equation for $\phi $ .


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