# Which electric field does E represents in the Ionospheric Dynamo Current equation?

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?

## 1 Answer

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 $$\phi$$ .