The question asks me to consider a capacitor consisting of two parallel conducting plates 1 and 2 with a dielectric material between them. (full description of system in attached file) There is also a free chargedensity between the plates. the question then asks me to show that the potential in the region a<z<2a (a point between the plates) is shown to be a given equation (shown in file) so basically a system is described and an potential equation is supplied and I have to show how that equation is derived? I have supplied all the relevant associated equations I can think of that may be required I just don't know how to bring them all together to produce the required (given) equation. Please can you show me your working. Thank you.

Q2)

Consider a capacitor consisting of two parallel conducting plates, 1 and 2, separation a, with a dielectric material of constant relative permittivity ε between the plates. Plate 1 is in the z = a plane and is held at a fixed potential V1, whereas plate 2 is in the z = 2a plane and is held at the fixed potential V2. The plates are so large compared to their separation that the electric field between them can be considered to depend only on z. Between the plates there is a free charge density where K is a constant.

i)
Show that the potential in the region a < z < 2a is,

ii)
Hence determine the electric field E in the region a < z < 2a between the plates.

... 13. Capacitance of a parallel plate capacitor with a conducting slab (of thickness less than the gap between the plates) introduced between the plates. ...

...conducting planes. The reciprocal system that we can use (since we know all about it) is that of a parallel plate capacitor with no charge between the plates. ...

... 1. A parallel-plate air capacitor has a ... 12 V b. Remember that the capacitance is proportional to the surface area of the conducting plate and inversely ...

... A large parallel plate capacitor is made up of two plane conducting sheets with seperation D, oneo f which has a small hemispherical boss of radius a on its ...

... charge is located a short distance above a large conducting horizontal plane ... uF capacitors forming two groups, each consisting of two capacitors in parallel. ...

... The rightmost configuration is two capacitors in parallel... the equivalent capacitance for the parallel case Cp ... A head is (approximately) a conducting sphere of ...

... straight wire is in the same plane as a rectangular, conducting loop. ... Three parallel plate capacitors, each having a capacitance of 1.0 μF are connected in ...

... All these wires have negligible mass and resistance. The rod is a distance r above a conducting cable. ... 7. A parallel plate capacitor with plates of area A ...

... of the molecules (transverse waves) or parallel to the ... a (displacement) current between the capacitor plates, there must ... Let us consider a conducting sheet of ...

... to connect the transistor and capacitor components of ... The FlexStar system uses Parallel Wafer Processing technology to ... are used to etch conducting films, such ...