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Electrostats Problem

  1. Nov 18, 2007 #1
    [SOLVED] Electrostats Problem

    1. The problem statement, all variables and given/known data
    Electrostats

    [​IMG]



    A wall has a negative charge distribution producing a uniform horizontal electric field. A small plastic ball of mass 0.01 kg, carrying a charge of -80.0 uC, is suspended by an uncharged, nonconducting thread 0.30 m long. The thread is attached to the wall and the ball hangs in equilibrium in the electric and gravitational fields. The electric force on the ball has a magnitude of 0.032 N.

    a. On the diagram below, draw and label all the forces acting on the ball:
    (picture of x and y axis with ball at center)

    b. Calculate the magnitude of the electric field at the ball's location due to the charged wall and indicate its direction relative to the coordinate axes.

    c. Determine the perpendicular distance from the wall to the center of the ball

    d. The string is now cut
    i. calculate the magnitude and direction of the acceleration of the ball relative to the coordinate axes
    ii. describe the resulting path of the ball


    2. Relevant equations
    1. E = F/q (electric field)
    2. F = ma
    3. E = V/d (electric field)



    3. The attempt at a solution

    a. Ft (tension) drawn in the second quadrant at an angle similar to the angle the string makes with the wall pointed away from ball, mg along the -y axis pointed away from ball, and Fe (electric) along the +x axis pointed away from ball

    b. E = F/q = (.032N)/(80x10^-6C) = 400 N/C, pointing left horizontally towards the wall

    c. not sure about this one, I have E = V/d => d = V/E, except I don't know where to begin to find the potential difference, perhaps an easier way...

    d. i. Fnet = sqrt[(.032N)^2 + (.98N)^2] = .98 N = ma = (.01kg)a => a = 98 m/s^2, directed in 4th quadrant along Ft (tension)

    ii. um southeast and away from the ball?
     
    Last edited: Nov 18, 2007
  2. jcsd
  3. Nov 18, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You need to figure out the angle the string makes. To do that, set up the equations for static equilibrium.

    Careful. The mass is 0.01 kg. What is mg?
     
  4. Nov 18, 2007 #3
    Wow, I totally ignored the equilibrium condition. So just thinking it through theoretically, the angle should be given by arctan(Fe/mg) right? And mg should be .098 :rolleyes:.
     
  5. Nov 18, 2007 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Right.
     
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