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Two spheres in equilibrium.

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Two small spheres, each of mass 2.00 g, are suspended by
    light strings 10.0 cm in length. A uniform
    electric field is applied in the x direction. The spheres
    have charges equal to -5.00 x 10^-8 C and +5.00 x
    10^-8 C. Determine the electric field that enables the
    spheres to be in equilibrium at an angle theta= 10.0° to the vertical.

    2. Relevant equations
    F=Eq,F=KqQ/r^2


    3. The attempt at a solution


    For the equilibrium of whole system, I have applied the forces along the x-axis.
    So then attraction force between two charges=The sum of forces on (-) and (+) charges by the field.And I have noticed that tensions are canceling each other.

    (8.99x10^9)(5x10x10^-6)^2/(2x0.1sin10)=2E(5x10^-6)
    and I have got E=6.47 x 10^3 N/c for the answer but unfortunately answer was incorrect.
    Was there any thing wrong with my equations?
    Thanks.
     
    Last edited: Aug 24, 2010
  2. jcsd
  3. Aug 24, 2010 #2
    i Dont get ur questions properly. What is the distance between the two spheres? is the angle 10degrees from vertical?
     
  4. Aug 24, 2010 #3
    Oh sorry about that yes that is 10 degrees from vertical.
     
  5. Aug 24, 2010 #4
    Eq=kq^2/(20sin10)^2+Tsin10..........1
    mg=Tcos10.........2
    Solving these two equations u should be able to get the answer.
     
  6. Aug 24, 2010 #5
    Ok thanks for it.
    But could you please tell me know is there any thing wrong with this statement.
    For the equilibrium of whole system, I have applied the forces along the x-axis.
    So then attraction force between two charges=The sum of forces on (-) and (+) charges by the field.And I have noticed that tensions are canceling each other.
     
  7. Aug 24, 2010 #6
    can u give me a diagram of the arrangement because in I assumed electric field to be in the left directrion and positive charge in the left and the negative charge in the right. Is that right???
     
  8. Aug 24, 2010 #7
    Negative charge is in the left and postive is in the right.And electric field is in the positive x direction.
    Unfortunately I can't provide the diagram.Sorry.
     
  9. Aug 24, 2010 #8

    rl.bhat

    User Avatar
    Homework Helper

    In the equilibrium position, net force acting on the spheres is the sum of electrostatic force and force due to the electric field. In this position the separation between the sphere is given by r = 2Lsinθ.

    Ιf T is the tension in the string, then

    Tcosθ = mg and

    Tsinθ = kq^2/r^2 + Eq.

    Now solve for E.
     
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