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 2.4 m2 (this is the area of one flat surface of the disk). Use the value 8.85e-12 C2/(N·m2) for 0.The charge Q1 = 5e-8 coulombs, and the charge Q2 = 3e-7 coulombs.

a. What is the potential difference VC - VB?
VC - VB = ______v

b. What is the potential difference VF - VD?
VF - VD =______v

c.What is the potential difference VG - VA? VG - VA =___________v

The charged disks have tiny holes which allow a particle to pass through them. An electron which is traveling at a fast speed approaches the plates from the left side. It travels along a path from A to G. Since no external work is done on the system of plates + electron,

K + U = Wext = 0

Consider the following states: Initial, electron at location A. Final, electron at location G.

d. What is the change in potential energy of the system?
U = ___________ joules

e.What is the change in kinetic energy of the electron?
K = _________ joules

Explanation / Answer

E= sigma/epsilon

sigma1=  5e-8 / 2.4 = 2.08333333e-8

sigma2=3e-7 /2.4 = 1.25e-7

E1=2.08333333e-8 /  8.85e-12 = 2354 N/C

a) VC - VB = - 2354N/C x 0.004m = - 9.41600 v

b) E2= 1.25e-7 /   8.85e-12 =14124 N/C

VF - VD =14124 N/C X 0.0017m = 24.0108 v

C)since there is no electric field between conductors,

  VG - VA =    VF - VD +  VC - VB =   24.0108 v   - 9.41600 v = 14.5948 v

d) delta U = -e ( VG - VA )= -14.5948 eV = -2.338 x 10-18 J

e)K + U = Wext = 0

So K= - U = 2.338 x 10-18 J

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