1. for a charge Q=+25 uC A. rank the electric energy between Q and q for a charg

Question

1. for a charge Q=+25 uC
A. rank the electric energy between Q and q for a charge q=+10 uC placed at points A-F big to small
B. rank the electric energy between Q and q for a charge q=+3 uC placed at points A-F
C. rank the electric energy between Q and q for a charge q=+100 uC placed at points A-F
2. explain your reasoning for your rankings

   for a charge Q=-25 uC
3. a. rank the electric energy between Q and q for a charge q=+10 uC placed at points A-F
b. rank the electric energy between Q and q for a charge q=+3 uC placed at points A-F
c. rank the electric energy between Q and q for a charge q=+100 uC placed at points A-F
4. explain your reasoning for your rankings

Explanation / Answer

Electrical energy between two charges Q and q is given by

U=KQq/r

where K =1/4pieo =9*109

Let each scale on x-axis represent

1 unit =1 m

on y-axis 1 unit =1 m

a)

Now q=10 uC

distance from Q to q at point A is

r=sqrt[32+32]=4.24 m

at point B

r=sqrt[22+22] =2.83 m

at point C=>r=3 m

at point D =>r=1 m

at point E =>r=1 m

at point F =>r=3 m

Now electrical energy at each point

UA =(9*109)(25*10-6)(10*10-6)/4.24 =0.53 J

UB= (9*109)(25*10-6)(10*10-6)/2.83 =0.795 J

UC=(9*109)(25*10-6)(10*10-6)/3 =0.75 J

UD = (9*109)(25*10-6)(10*10-6)/1 =2.25 J

UE=(9*109)(25*10-6)(10*10-6)/1 =2.25 J

UF=(9*109)(25*10-6)(10*10-6)/3=0.75 J

So UD=UE>UB>UC=UF>UA

b)

Now q=3 uC

UA =(9*109)(25*10-6)(3*10-6)/4.24 =0.16J

UB= (9*109)(25*10-6)(3*10-6)/2.83 =0.24 J

UC=(9*109)(25*10-6)(3*10-6)/3 =0.225 J

UD = (9*109)(25*10-6)(3*10-6)/1 =0.675 J

UE=(9*109)(25*10-6)(3*10-6)/1 =0.675 J

UF=(9*109)(25*10-6)(3*10-6)/3=0.225 J

So UD=UE>UB>UC=UF>UA

c)

Now q=100 uC

UA =(9*109)(25*10-6)(100*10-6)/4.24 =5.3 J

UB= (9*109)(25*10-6)(100*10-6)/2.83 =7.95J

UC=(9*109)(25*10-6)(100*10-6)/3 =7.5 J

UD = (9*109)(25*10-6)(100*10-6)/1 =22.5 J

UE=(9*109)(25*10-6)(100*10-6)/1 =22.5 J

UF=(9*109)(25*10-6)(100*10-6)/3=7.5 J

So UD=UE>UB>UC=UF>UA

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