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PLEASE answer all the subquestions. Thank you so
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8. Consider two infinite rectangular slabs of Ohmic material and a current that flows perpendicular to the boundary between them. The two slabs have conductivities given by o1 and 02. The 02 1: J2 01 a current densities in the slabs are indicated. This exercise will use the matching conditions for electric fields and potentials above and below the boundary between two media. The electric fields satisfy E above – E below = - ñ EO where here a is the surface charge density on the boundary between the media and în is the normal vector from the surface below to the surface above. a) Describe why, in a steady state, the two current densities are equal. b) Use the current densities to determine an expression for E2 – Ei (where these are the electric fields in the two media) in terms of the current density in the lower material. Show that this implies that there is a non-zero charge density between the two
surfaces and determine an expression for this charge density. c) Given a patch in the boundary of surface area A, determine an expression for the charge on this surface in terms of the current I that flows through the surface. d) Use the result from the previous part to relate the charge at the boundary to the current for the case where the lower material is a perfect conductor. Suppose that material 2 were sandwiched between two conductors. Determine a relationship between the capacitance of the arrangement and the resistance of material 2.