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Electrostatics with 2 charged masses on string help?

  1. Mar 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Two identical spheres having the same mass, m = 0.60 kg and the same positive charge, q, are suspended from the same point by strings of length 20.0 cm:

    (a) What charge q resides on each sphere?

    (b) The apparatus above is now placed in an upward directed
    but unknown electric field. The angle, measured from the vertical from which the strings hand is 45°. What is the value of E?

    2. Relevant equations

    (\vec{F}_{net})_x = \Sigma F_x = 0
    (\vec{F}_{net})_y = \Sigma F_y = 0

    F_e = k \frac{q^2}{r^2}

    [tex]\tan \Theta = \frac {T_x} {T_y}[/tex]

    3. The attempt at a solution

    Alright, for part a), I did the sum of the forces for 1 mass (1 side of the triangle).
    In the y direction were Ty - mg = 0, so therefore Ty = mg
    Then I did Tx - Fe = 0, so therefore Tx = Fe

    Since it's a right triangle, I set up
    [tex]\tan \Theta = \frac {T_x} {T_y} = \frac {F_e} {mg} = 0[/tex]
    So Fe came out to be around 3.39N
    Finally I plugged all the numbers into the Fe equation and solved for q and got 1.94x10^-6 C which I think is correct.

    But for part b), I'm a little more confused. The constant E field is being directed vertically upwards. But what happens to the force in the x direction on the charges? If the E field were horizontal, I think I'd just let the Force in the x direction be equal to qE, while the vertical sum of forces remains Ty - mg = 0. But, since the E field is vertical, I assume that I can't let the force in the x direction just be qE as it's perpendicular to the E-field? My thinking is that there will be an E-field there as there is an electric force there still (Tx has to be balanced out with something to produce that max angle), but that it won't be the E field that the question is asking for, just the E field produced by the other charge. Knowing that there will be a qE going in the vertical which is the E I would want, that would make it too many variables to solve for. 2 different E's and of course the tension I'd then need to know to solve them.

    So another thing I was thinking was trying a little superposition instead on the whole triangle system. Let the E field of both charges be directed along their Tension forces, and then find the resultant vector they make above the triangle, which will be a vertical line going "up". Then let the sum of that resultant vector and the gravity pointing down equal to zero? And then solve for E. But it just doesn't seem right. What about the tension? And isn't this still just the E field caused by the 2 charges themselves, and not the external E field that the question wants?

    So I'm not too sure on the correct way to conceptualize what's going on with the external Electric field and electric field between the charges themselves. How do they relate to this static equilibrium problem. Thanks for any help!
  2. jcsd
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