Question: Initial Plate 1 d Conductor Plate 2 |'/ Final 0i Plate 1 I 9% \\ ' 0' lConductor " 02 Plate 2 Figure 1. Initially two thin uncharged plates are separated by a distance d and connected by a conductor. The top plate is Plate 1 and the bottom is Plate 2. Then an identical but charged plate with surface charge 0' is inserted a distance d/3 under Plate 1 which induced a surface charge density 0'1 and 0'; on Plate 1 and Plate 2 respectively. Two very thin conducting plates are separated by a distance d. They are connected with a conducting wire. They have identical, large surface areas so any end effects can be neglected and the wire is so thin 0.6. its capacitance is so small) that charges in it will have negligible electric effect. Initially the plates are not charged. A charged, thin, nonconducting plate with surface charge density a is then inserted between the two plates, a distance d/3 below plate 'I (the top plate) and 261/3 above plate 2 (the bottom plate). This induces a surface charge density 0'] on plate 'I and surface charge density 02 on plate 2. Give expressions in terms of 6'0 , not Coulomb's constant. Part 1) Write an expression relating 0'1 to 0'2. 61: Pa rt 2) Ea 01 d \"Eb /3 l 0 .. 2:." EC 4 q vEd Figure 2. The electric field vectors in the spaces above, below and between plates are shown in the figure. Represent the electric fields above, below and between the plates as shown in the diagram. In terms of these electric fields, write down an expression for the voltage difference between the inserted plate and Plate 1. Part 3) 01 Plate 1 Inserted \"0 Plate 02 Plate 2 Figure 3. Three charged plates of charges 01 0' and 62 and separated by distances 61/3 and 261/3 respectively. The top and bottom plates are connected by a conductor. Come up with an expression for 0'1 in terms of 0'. 61: Hint: There are a number of ways you can approach this question. One way is to consider the electric fields around the plates, use Gauss's law to write expressions to relate these to the charge densities. Also think carefully about what the potential difference between plates 1 and 2 are. Write an expression to express this