The space between two parallel conducting plates each having an area S is filled with an i...

The space between two parallel conducting plates each having an area S is filled with an inhomogeneous ohmic medium whose conductivity varies linearly from σ1 at one plate (y = 0) to σ2 at the other plate (y = d). A d-c voltage V0 is applied across the plates as in Fig. Determine

a) the total resistance between the plates,

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b) the surface charge densities on the plates,

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c) the volume charge density and the total amount of charge between the plates.

Figure: Inhomogeneous ohmic medium with conductivity σ(y)