Three charged metal disks are arranged as shown (cutaway view). The disks are he

Question

Three charged metal disks are arranged as shown (cutaway view). The disks are held apart by insulating supports not shown in the diagram. Each disk has an area of 2 m^2 (this is the area of one side of the disk). (a) Calculate the potential difference V_C-V_A. Clearly show every step in your work. Your work should include clearly indicating and labeling all relevant fields and paths. (b) Now a large neutral slab of plastic, with dielectric constant 4.5, is inserted between the the two rightmost disks. The plastic slab completely fills the gap between the disks. Calculate the potential difference V_C-V_A. Clearly show every step in your work. Your work should include clearly indicating and labeling all relevant fields and paths.

Explanation / Answer

Magnitude of electric field on a metallic charge conductor = sigma/2Epsilon_0
where sigma is the charge density of the plate
sigma 1 = 1.2*10^-7/2
sigma 2 = 7 *10^-8 /2

Electric field of plate 1 = -1.2*10^-7/(2*2.5*8.85e-12)
Electric field of plate 2 left side = sigma/Epsilon_0
= 1.2*10^-7/(2*8.85e-12)
Electric field of plate 2 right side = 7*10^-8 /(2*8.85e-12)
Electric field of plate 3 = -7*10^-8/(2*2*8.85e-12)

Electric field in region left = 1*-2*10^-7/(2*8.85e-12) directed right
Electric field in region right = 1*-7 *10^-8 /(2*8.85e-12)

|Vc-Va| = 1*-2*.0045*10^-8/(2*8.85e-12) = 2.5568 volts

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