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Charge in conductors

  1. Aug 13, 2012 #1
    1. The problem statement, all variables and given/known data
    A sphere conductor of radius 18 cm has potential 27 Volt. Another sphere conductor has potential 18 Volt. Both of them are connected and the combined potential is 24 Volt. Find:
    a. the charge of second sphere
    b. the charge of each sphere now


    2. Relevant equations
    Q = CV
    V = kQ / r

    3. The attempt at a solution
    a.
    V1 = k.Q1 / r1
    27 = 9 x 109 x Q1 / (18 x 10-2)
    Q1 = 5.4 x 10-10 C

    Then I don't know how to continue.....:grumpy:
     
  2. jcsd
  3. Aug 13, 2012 #2

    AGNuke

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    Gold Member

    Try using conservation of charge.

    EDIT: Are those two sphere of same radius?
     
  4. Aug 13, 2012 #3

    ehild

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    You can calculate also the final charge Q1' on the first sphere, as its potential is known.
    As for the second sphere, kQ2/R2=18 and kQ'2/R2=24. From here, you can find the ratio Q2'/Q2. As AGNuke said, the sum of the charge on the spheres is conserved: Q1+Q2=Q1'+Q2'.

    ehild
     
  5. Aug 13, 2012 #4
    I don't know but maybe they are not

    V' = k Q1' / r1
    24 = 9 x 109 x Q1' / (18 x 10-2)
    Q1' = 4.8 x 10-10 C

    kQ2/R2=18 ; kQ'2/R2=24
    So Q2'/Q2 = 24/18 = 4/3

    Q1+Q2=Q1'+Q2'
    5.4 x 10-10 + Q2 = 4.8 x 10-10 + 4/3 Q2
    Q2 = 1.8 x 10-10 C

    Q2' = 2.4 x 10-10 C


    If the spheres have same radius, then the combined potential should be: (27 + 18)/2 = 45/2 V. Am I correct in this case?

    Thanks
     
  6. Aug 13, 2012 #5

    ehild

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    Your solution is excellent and you are right, if the radii were the same the final voltage would be 22.5 V.

    ehild
     
  7. Aug 14, 2012 #6
    OK. Thanks a lot :smile:
     
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