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Electrostatics: suspended spheres

  1. Jul 19, 2004 #1
    Two small spheres of mass m are suspended from strings of length L that are connected at a common point.

    One sphere has charge Q, the other has 2Q.

    The strings make angles (theta1) and (theta2) with the vertical.

    (a) How are theta1 and theta2 related?

    (b) Assume theta1 and theta2 are small. Show that the distance r between the spheres is

    [tex]r \approx \frac {4k_eQ^2L}{mg} [/tex]
    supposed to be a paren around the whole fraction... :uhh: the whole thing raised to 1/3 power

    Thanks very much for answering :)
     
    Last edited: Jul 19, 2004
  2. jcsd
  3. Jul 21, 2004 #2
    because of the third newton's law and considering coulombs law -->
    Tsin(theta_1)=2K(Q^2)/(R^2)=Tsin(theta_2)--> theta_1=theta_2=theta
    working on the vertical axis --> Tcos(theta)=mg....(1) and on horizontal axis
    Tsin(theta)=2K(Q^2)/(R^2)....(2) now dividing (2)/(1)-->
    tan(theta)=2K(Q^2)/(mg*(R^2)) and because theta_1=theta_2-->
    sin(theta)=(R/2)/L=R/2L, according to the condition of theta being small-->
    sin(theta)~(theta)~tan(theta)--> R/2L~2K(Q^2)/(mg*(R^2))-->
    (R^3)~4KL(Q^2)/mg. check dimensions and you'll see that r suppose to be (r^3)
     
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