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Homework Help: Potential difference, angles

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A small sphere with mass .015kg hangs by a thread between two parallel vertical plates .05m apart. The plates are insulating and have a uniform surface charge densities +σ and -σ. The charge on the sphere is q = 8.9 x 10^-6 C. What potential difference between the plates will cause the thread to assume an angle of 30 degrees with the vertical?

    2. Relevant equations
    some formulas in the chapter and on a previous chapter. im not sure which ones are useful:
    dV = -Edl
    Ua - Ub = q(Va - Vb)
    Kb = Ka + Ua - Ub
    Kb = .5mv^2
    Va - Vb = Ed
    F = qE
    p = qd
    Torque = pEsinθ
    Torque = p X E

    3. The attempt at a solution

    I am clueless. the only thing i know is Ka = 0 because it started at rest. that means Kb/q = Va - Vb
    but then again the velocity at Kb would = 0 wouldnt it? so I dont know. do I find the F by figuring out E somehow? or does it have something to do with Torque? i dont know how to find p (electric dipole moment). so yea im lost, any help would be appreciated

    I think it has something to do with the gravity pulling down then the E pulling/pushing to the side.
  2. jcsd
  3. Oct 16, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Think of this as a statics problem, where one of the forces is the electric force. What forces act on the sphere? What is the net force?
  4. Oct 16, 2008 #3
    ok so does that mean F = qE is pushing to the side and gravity pushing down?

    edit: o wait. Va - Vb = Ed.

    the equation of E i beleive is this: E = qσ/2πε(.025^2)
    we have all that accept σ. d is just .025m (correct me if im wrong on any of this).

    then i guess you use F = qE + gravitational force and set the angle to 30 degrees, then solve for σ. then plug that into Ed to get the answer of Va - Vb right?

    somethign isnt right, im not coming out with the right answer :(
    Last edited: Oct 16, 2008
  5. Oct 16, 2008 #4
    ok how can i find net force? and is E = qσ/2πε(.025^2) the correct equation for E?

    i did E = qσ/4πε(.025^2) + qσ/4πε(.025^2) = qσ/2πε(.025^2)
  6. Oct 16, 2008 #5

    Doc Al

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    Staff: Mentor

    Yes. Don't forget the string tension.

    You'll need that.

    You won't need that to answer the question.

    The first thing to do is to solve for the electric force on the sphere, using statics. Once you have the force, you can figure out the field needed and then the potential difference.

    You don't need any equation that contains σ.
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