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Calculate charge on object suspended between capacitor plates

  1. Jul 16, 2013 #1
    1. The problem statement, all variables and given/known data

    It would be greatly appreciated if someone could check over my work. It is very likely that I made mistakes. If I made any mistakes, could you please tell me where I went wrong? Thank you. I will use this problem to study for my next exam. I have also attached a figure that I created that goes with this problem. Thanks again.

    As shown in the Figure, a 30mg object with a charge q is suspended with a light string in a uniform electric field between the plates of a charged capacitor. The capacitance of the capacitor is 1mF, the separation between the parallel plates is 4.0cm and the charge (Q) on the capacitor is 1.25C. Calculate the charge q on the 30 mg object, when the suspension thread holding the charged object is in static equilibrium at an angle of 10 degrees with respect to the vertical.

    15mlmv5.jpg

    C=1.0x10^-3 F
    d= 4.0x10^-2 m
    m= 30.0x10^-3 g
    Q= 1.25C
    θ= 10 degrees

    2. Relevant equations

    C=Q/V, E=V/s, q=FE

    3. The attempt at a solution

    ƩFx=0
    ƩFy=0
    Ty=mg
    Tx=F

    Ty=(30.0x10^-3g) * (9.8)
    Ty= .294 N

    cos(10)= .294N/T
    T= .294N/.9848
    T= .298535N

    sin(10)=Tx/T
    sin(10)=Tx/.2985
    Tx=.05184N
    Tx=F
    F=.05184

    C=Q/V
    V=Q/C
    V=1.25C/(1.0x10^-3F)
    V=1.250x10^3V

    E=V/s
    E=(1.250x10^3V)/(4.0x10^4 m)
    E= 3.125x10^4 v/m

    q=F/E
    q= .05184 N/ (3.125x10^4 v/m)
    q= 1.658x10^-6 C
     
  2. jcsd
  3. Jul 16, 2013 #2

    gneill

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    Check your conversion for mg to kg. Otherwise, your method looks okay.
     
  4. Jul 17, 2013 #3

    rude man

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    Looks like the OP used the correct magnitude for mass, he/she just used g instead of kg for the unit designator.
     
  5. Jul 17, 2013 #4

    gneill

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    Perhaps, but the resulting order of magnitude of the y-component of the tension, Ty, is incorrect.
     
  6. Jul 17, 2013 #5

    rude man

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    Why? Ty = mg = 30e-3 * 9.8 = 0.294N.
     
  7. Jul 17, 2013 #6

    gneill

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    30mg = 30 x 10-3 grams = 30 x 10-3 x 10-3 kg = 3.0 x 10-5 kg

    30mg x g = ?
     
  8. Jul 17, 2013 #7

    rude man

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    Right you are. That is a mighty light mass! I was thinking 30g, obviously. Thanks.
     
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