Question

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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 of2.2 m2 (this is the area of one flat surface of the disk). Use the value 8.85e-12 C2/(N·m2) for ε0.The charge Q1 = 3e-8 coulombs, and the charge Q2 = 3e-7coulombs.




What is the magnitude of the electric field in the region between disks 1 and 2?
E|12| = V/m - 1)



What is the potential difference VC - VB?
VC - VB = volts 2)


What is the potential difference VD - VC?
VD - VC = volts 3)


What is the potential difference VF - VD?
VF - VD = volts 4)


What is the potential difference VG - VF? VG - VF =( )volts 5)


What is the potential difference VG - VA? VG - VA =( )volts 6)



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 leftside. It travels along a path from A to G. Since no external work is done on the system of plates + electron,
ΔK + ΔU = Wext = 0
Consider the following states: Initial, electron at location A. Final, electron at location G.


What is the change in potential energy of the system?
ΔU = joules (7)


What is the change in kinetic energy of the electron?
ΔK = joules (8)

Answer 1

Capasitors equation: C = ?A/d

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for disk 1 and 2:

C = ?*(2.2)/(0.004) = 8.85e-12*2.2/0.004 = 4.87e-9 F

V=Q1/C = 3e-8/4.87e-9 = 6.16 Volts

E|12| = V/d = 6.16/0.004 = 1.54e3 Volts/m

(We could use Gauss' law to find E, the result is 1.54e3 Volts/m)

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We found V above:

VC - VB = -6.16 volts

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the potential difference VD - VC is zero, because according to the Gauss' law the electrical field inside the metal is zero

VD - VC = 0

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for disk 2 and 3:

C = ?*(2.2)/(0.0017) = 8.85e-12*2.2/0.0017 = 11.453e-9 F

V=Q2/C = 3e-7/11.457e-9 = 26.19 Volts >>>> VF - VD = 26.19 Volts

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the potential difference VG - VF is zero, because according to the Gauss' law the electrical field inside the metal is zero

VG - VF = 0

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VG-VA = VG (-VF VF) (-VD VD) (-VC VC) (-VB VB) - VA

= (VG - VF) (VF - VD) (VD - VC) (VC - VB) (VB - VA)

= (0) ( 26.19) (0) (-6.16) (0)

= 26.19 - 6.16

= 20.03 Volts

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the potantial diffrence between A and G is: VG-VA (= 20.03 Volts)

?U = q*V = (-1.6*10e-19)*(20.03) = -32.048 Joul

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According to the conservation of energy, Wext = 0 :

?K ?U = Wext = 0 >>>> ?K = -?U

?K = - (-32.048) = 32.048 Joul

Answer 2