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Electric Charge Applied on Two Wires of Electroscope?

  1. Sep 4, 2015 #1
    1. The problem statement, all variables and given/known data
    A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 24-g spheres at the ends. When charged, nearly all the charge resides on the ends of the spheres. (See diagram attached)

    If the wires each make a 26° angle with the vertical, what total charge Q must have been applied to the electroscope? Ignore the mass of the wires?

    Diagram of the Electroscope:
    Capture_zpsbv8hndvn.png



    2. Relevant equations
    What does it mean to ignore the mass of 24g? Does that mean that I can find the charge by finding the distance between the two points?

    3. The attempt at a solution
    I split the triangle into two right triangles. Then I used the trig properties to deduce that:

    sin26° = opp/hyp = .4387, opp/78cm = .4387 = opp =.4387*(78cm) =34cm
    cos26° = adj/hyp = .8988, adj/78cm = .8988 = adj =.8988*(78cm) =70cm

    Now using this data, I would input the distance between the repelling positive charges into the Coulombs Law:

    F = (k|Q1||Q2|)/(r12)^2 Where k = 8.988x10^9 N*m^2 / C^2 and r = 68 which is derived above
    (34*2) = 68 cm or 68*10-2m

    How do I find the value of Force? I will be needing it to complete the problem this way. Thank you!

    Capture_zpskxn4o4n9.png
     
  2. jcsd
  3. Sep 4, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You are to ignore the mass of the wire, not the spheres. You'll need their mass to solve the problem.

    Analyze the forces acting on each sphere. Hint: Three forces act.
     
  4. Sep 4, 2015 #3
    Is the method I am using thus far correct to find the value of the Q? Since there is no mention of an electric field in this problem I assume I will be using the coulombs law equation I stated above: [tex] k\bullet\mid Q_1\mid\bullet\mid Q_2\mid\\r_{1,2}^2[/tex]
     
  5. Sep 5, 2015 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Sure, you need to use Coulomb's law to calculate the total charge. (Note that Q_1 = Q_2 = Q/2.)

    But you first need to do the force analysis to find the electrostatic force.
     
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