# Electric field of a capacitor in dielectric medium with weird size

I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between the plates, the permittivity of the dielectric is epsilon.Find the electric field inside the dielectric. The second one is when the dielectric only covers half the area. First picture (Symbols are E1,E2,Epsilon for clarification) Again,What is the Electric field in the dielectric?Express In terms of Q A(area) epsilon0 and epsilon . How do we go about solving this problem?Is there anything to do with boundary conditions?

• Sorry for the crap drawings – el psy Congroo Mar 3 '14 at 23:22
• To do this you need to seperate the capacitors depending on the position of the dielectric in them. For the first image the capacitor is equivalent to two capacitors in series, one with the empty space and one with only the dielectric (your area would be halved for each one). The second image will be exactly the same except the two capacitors must be in parallel rather than in series. – Carterini Mar 3 '14 at 23:51
• Have you tried viewing the system as a pair of distinct capacitors in series or in parallel. It sounds weird, but it will work. (On the other hand, it will not give you all the physics of the situation.) – Emilio Pisanty Mar 3 '14 at 23:55