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Electric Field and a Charged Cork Ball on a Massless String

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data
    A charged cork ball of mass 1g is suspended on a light string in the presence of a uniform electric field. When E = (3i + 5j) * 10^5 N/C, the ball is in equilibrium at [tex]\theta[/tex] = 37 degrees. Find the charge on the ball and the tension on the string.

    ====================
    |\
    |[tex]\theta[/tex]\
    | \
    | \ / <- uniform electric field, E = (3i + 5j) * 10^5 N/C
    | \/
    | O <- charged cork ball, mass = 1g, q = ?


    i
    ^
    |
    |
    -------> j

    2. Relevant equations
    F(electric) = qE
    F(grav) = mg(-j)


    3. The attempt at a solution
    I tried using the cosine law with the forces to isolate for [tex]\theta[/tex]
    a^2 = b^2 + c^2 -2bc * cos([tex]\alpha[/tex])
    but it canceled out.
    Anyways,
    [tex]\alpha[/tex] = [tex]\theta[/tex]
    a = F(elec)
    b = F(grav)
    c = F(res) = F(elec) + F(grav)

    Any ideas? Thanks!
     
  2. jcsd
  3. Sep 24, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    In the equilibrium position, resolve mg into two components.
    mg*cosθ will provide the tension and mg*sinθ will try to bring the string into vertical position.

    The magnitude of the electric field is sqrt(34) and makes an angle α = arctan(5/3)
    The electric force on the cork ball is q*E.
    In the equilibrium position angle between the string and the electric force is (90 +α - θ )
    Its component along the string is Fe*cos(90 +α - θ) and perpendicular to the string is Fe*sin(90 +α - θ ).
    Equate them with the components of mg and solve for T and q.
     
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