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Two conductors connected by a thin wire

  1. Aug 10, 2014 #1
    The problem is :


    The conducting spheres (s1) of radius R and (s2) of radius 2R of the figure shown are connected by a thin wire. The conducting sphere (s3) of radius R is connected to ground. A charge Q is placed on the sphere (s1).

    1- Determine the charges Q1,Q2,and Q3 thus distributed on the 3 spheres (s1),(s2) and (s3) respectivly.
    2- Determine the respective potentials v1 and v2 on spheres (s1) and (s2).
    3- Determine the self capacitance C of the group of spheres (s1) and (s2).
    4-determine the coefficient of influence C' between the group of spheres (s1) and (s2) and sphere (s3).
    5- The thin wire is now cut at points of contact with the two spheres (s1) and (s2),in moving sphere (s3) (always connected to earth) away from the spheres(s1) and(s2). What wouid then become :
    a- The charges on (s1),(s2)and (s3)?
    b-The potentials of (s1) and (s2)?

    I solved question 1 in this way but I'm not sure about the solution:
    1- v1=Q1/4∏εR +Q2/4∏ε(20R) +Q3/4∏ε(40R).
    v2=Q1/4∏ε(20R) +Q2/4∏ε(2R) +Q3/4∏ε(20R).
    as (s1) and (S2) are connected by a thin wire then:v1=v2...(1)
    we can say that Q=Q1+Q2...(2)
    v3=Q3/4∏εR +Q2/4∏ε(20R)+Q1/4∏ε(40R)=0....(3)

    what I finally get is : Q1=(722/2239)Q, Q2=1517/2239)Q, Q3=-(939/22390)Q

    Is condition (1) right ? since in question 2 he asked to determine v1 and v2. (or it is a trick?)

    If anybody can help to be sure about my answer and complete the problem.
    the figure is in the attachment.
     

    Attached Files:

  2. jcsd
  3. Aug 10, 2014 #2

    mfb

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    Well, you don't have to solve them in the given order, but plugging in the calculated charges to get the potentials is still an additional step.
    Maybe in (1) you are allowed to ignore the small contributions to V1 and V2, then you can calculate Q1 and Q2 without the potentials.
     
  4. Aug 11, 2014 #3
    I didn't get what do you mean, if you can explain more?
     
    Last edited: Aug 11, 2014
  5. Aug 11, 2014 #4

    mfb

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    Which part was unclear?
     
  6. Aug 11, 2014 #5
    I didn't get it.
    simply my question is : Is condition (1) true (V1=V2) in my answer to question 1?
     
  7. Aug 11, 2014 #6

    mfb

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    V1=V2 is true, sure.
     
  8. Aug 12, 2014 #7
    :smile:ok thanks.
    Lets skip now to question 5,do you have any ideas to solve it ?
     
  9. Aug 12, 2014 #8

    mfb

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    After the wire is cut, the charges on the spheres [...]
     
  10. Aug 12, 2014 #9
    ok,where is the idea?
     
  11. Aug 12, 2014 #10

    mfb

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    That is the idea. What happens to those charges? Do they change?
     
  12. Aug 13, 2014 #11
    I think Q1 and Q2 will remain the same and Q3 will be 0 since (s3) is moved away and V3=0.
     
  13. Aug 13, 2014 #12

    mfb

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    Right.
     
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