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Homework Help: Easy electric field question please help

  1. Sep 6, 2005 #1
    okay here's my problem, and the work I've done is below it. might be kinda long, I'm sorry:
    Two small spheres, each of mass 3.00 g , are suspended by light strings 10.0 cm in length (see figure). A uniform electric field is applied in the x direction. The spheres have charges equal to -6.0 * 10 ^ -8 C and 6.0 * 10 ^ -8 C. Determine the electric field that enables the spheres to be in equilibrium at an angle of theta = 10 degrees. [diagram]

    Round your answer to three significant figures. Take the Coulomb constant to be 8.99 * 10 ^ 9 and the acceleration of gravity to be -9.8 m/s/s
    -----------work--------
    Positive charge = Q1, negative charge = Q2
    Consider all forces acting on Q1

    In the y-direction:
    force of gravity, 9.8 m/s/s * 0.003 kg = 0.0294 N
    Y-component of tension, T * cos10
    In equilibrium, forces are equal, T * cos10 = 0.0294 N, so 0.0294 N / cos 10 = T
    Magnitude of tension = 0.02985 N

    In the x-direction:
    force of Q2 on Q1, given by k * ( |Q1| * |Q2| ) / r ^ 2
    Where r is the 0.03472 meters, or the side length of the triangle that is formed by the two charges
    This force is = 9.321 * 10 ^ -5 N

    x-component of tension, which is T * sin10 or 0.00518 N

    both forces are to the left, and the other force to the right is the electric field acting on the positive particle.
    So -0.02985 N – 0.00518 N + F = 0
    F q2 on q1 tension due to electric field

    Set equal, you get the force due to electric field is equal to 0.006115 N
    or 6.115 * 10 ^ -6 kN

    since F = E / Q, we can multiply this F by Q2 and get the answer, right?
    (6.115 * 10 ^ -6 kN) * (6.00 * 10 ^ -8 C) = 3.669 * 10 ^ -13 kN/C
    Wrong answer…what’s the flaw in my logic? Thanks in advance
     
  2. jcsd
  3. Sep 6, 2005 #2

    lightgrav

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    T_x = -5.18 mN ; Fq_x = -.093 mN ,
    so F_x = 5.27 mN from E-field.
    T_vector is not in x-direction!
    (btw, I did not check your computations)
     
  4. Sep 6, 2005 #3

    mukundpa

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