Electromagnetism

amy

A plasma is described by the dielectric function
where  is a constant. Any attempt to establish a voltage
across the plasma generates a region of vacuum called the quot;sheathquot; on either side of the plasma volume.

Derive expressions for the uniform electric field  in the plasma and for  in the sheath. Assume that there is no free charge anywhere. Assume that  is small enough that an electrostatic approximation is always valid.

I don't really understand. Isn't the electric field is stated in the question already ?  

                                   Originally Posted by touqra                   A plasma is described by the dielectric function
where  is a constant. Any attempt to establish a voltage
across the plasma generates a region of vacuum called the quot;sheathquot; on either side of the plasma volume.

Derive expressions for the uniform electric field  in the plasma and for  in the sheath. Assume that there is no free charge anywhere. Assume that  is small enough that an electrostatic approximation is always valid.

I don't really understand. Isn't the electric field is stated in the question already ?                  
I would say that your task is to find the constants  and  in terms of  and

I'd say start with the Laplace equation - but unless you have some futher specification of the geometries involved like a sketch og something, that might prove tricky  

                                   Originally Posted by Troels                   I would say that your task is to find the constants  and  in terms of  and

I'd say start with the Laplace equation - but unless you have some futher specification of the geometries involved like a sketch og something, that might prove tricky                  
It's two plate of electrodes, one grounded, another at voltage V, separated by a distance
H + 2h, where h is the size of the sheath at each end of the electrode and H the size of plasma.  

    You have two different types of dielectric, one is vacuum, the other given by the plasma equation... Given the obvious direction of the electric field, what is the relationship between Es amp; Ep?

Now what is the relationship between the fields and the potential?
Solve to get the absolute fields.