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Finding the initial and final charge of two spheres

  1. Sep 6, 2011 #1
    1. The problem statement, all variables and given/known data


    Two identical small metal spheres with q1 > 0
    and |q1| > |q2| attract each other with a force
    of magnitude 70.2 mN, as shown.

    The spheres are then brought together until
    they are touching. At this point, the spheres
    are in electrical contact so that the charges
    can move from one sphere to the other until
    both spheres have the same final charge, q.

    After the charges on the spheres have come
    to equilibrium, the spheres are moved so that
    they are again 1.87 m apart. Now the spheres
    repel each other with a force of magnitude
    18.954 mN.

    Returned to original position
    A.)What is the final charge on sphere 2? The Coulomb
    constant is 8.98755 × 10^9N  m2/C2
    .Answer in units of µC
    002 (part 2 of 2) 10.0 points

    B.)What is the initial charge q1 on the first
    sphere?
    Answer in units of µ

    2. Relevant equations
    F=kq1q2/r^2
    x=-b(+/-)sqrt(b^2-4ac)/2a




    3. The attempt at a solution

    q1 is positive, q2 is negative

    F 12 = F 21 = 70.2 mN = -k(q1)(q2)/r²
    k = 1/((4)(π)(ε) = 8.9876 x 10^9 m²/c²

    70.2mN = -(8.9876 x 10^9)(q1)(q2)/1.87²

    after the spheres touch the charge on each sphere is qf = (q1 +q2)/2
    F = 18.954 x 10^-3 = (8.9876 x 10^9)(qf²)/1.87²
    qf = 2.716 uC
    A) 2.716 uC
    q1 = -q2 + 2*qf
    q1 = -q2 +5.432uC
    q1(q2) = 2.73 x10^-11
    -q2² + (5.43 x 10^-6)q2 +2.73 x 10^-11 = 0
    q2= -+2716 x 10^-6 +/- sqrt(2.95 x 10^-11 + 4(2.73 x 10^-11))/4 = +2.716 +/- 2.944 uC
    q2 is negative , so -.288 uC
    q1= 5.72 uC
    B).?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 6, 2011 #2
    You have answers for q1 and q2. I plugged them in and it looks like they are right. You appear to have answered parts A and B.

    ???????
     
  4. Sep 6, 2011 #3
    This is an online homework. It says I got A right but B is wrong. I will go back through and check my math. I just wanted to make sure the process was right.
     
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