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hunt_mat

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## Main Question or Discussion Point

Hi,

I am looking at a problem where I have two electrically conducting fluids where charge accrues on the interface, I know that one of the equations that I have to use comes straight from the usual boundary conditions for the normal component of the electric field, the other one apparent comes from integrating the continuity equation:

[tex]

\frac{\partial\rho}{\partial t}+\nabla\cdot\mathbf{J}=0

[/tex]

around a closed surface ending up with a covariant derivative, in all the papers I have seen the equation simply quoted and not derived, I am interested in it's derivation.

Can anyone suggest any papers or give be a few pointers?

Mat

I am looking at a problem where I have two electrically conducting fluids where charge accrues on the interface, I know that one of the equations that I have to use comes straight from the usual boundary conditions for the normal component of the electric field, the other one apparent comes from integrating the continuity equation:

[tex]

\frac{\partial\rho}{\partial t}+\nabla\cdot\mathbf{J}=0

[/tex]

around a closed surface ending up with a covariant derivative, in all the papers I have seen the equation simply quoted and not derived, I am interested in it's derivation.

Can anyone suggest any papers or give be a few pointers?

Mat