Question: 129 two large parallel plane conducting plates are a distance...
12-9 Two large parallel plane conducting plates are a distance d apart. The region between them is filled with two l.i.h. materials whose surface of separation is a plane parallel to the plates. The first material (with properties σ1 and Ɛ1) is of thickness x, while the second material (σ2, Ɛ2) has thickness d - x. There is a steady current between the plates that are kept at constant potentials of φ1 and φ2. Find the potential at the surface of separation of the two media, and the free surface charge density there.
The answers are:
Potential: [σ1(d - x)φ1 + σ2(x)φ2]/[σ1(d - x) +σ2(x)];
Free Surface Charge Density: (σ1*Ɛ2 - σ2*Ɛ1)(φ1 - φ2)/[σ1(d - x) +σ2(x)]
Please show all work.