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Electric Charges (max and min)

  1. Sep 6, 2011 #1
    A positive charge Q is on the y-axis at a distance a from the origin, and another positive charge q is on the x-axis at a distance b from the origin.
    A) For what values(s) of b is the x-component of the force on q a minimum?
    B) For what values(s) of b is the x-component of the force on q a maximum?

    Ok so I know that when b is zero, there is no x component.

    To solve the maz I did the following

    Fx=kQq/(a+b)^2

    soFx = (4πεQq/(a^2 +b^2))(b/dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3
    a^2 +b^2))= 4πεQqb/(a^2 +b^2)^1.5

    I took the deriviative of Fx with respect to b,
    dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3 (I don't know if this is right)
    to solve for b I got
    b=a/sqrt(8a^2q)^3

    I'm pretty sure this is not right since on the website I use to submit my homework, there is only one space below the a for the maxima.

    Where I need to input my answers it says the following:
    a) Minima when b=___ and also as b approaches infinity
    b) Maxima when b= +-a/sqrt____

    There's only space for one number on each blank. I assume a) is zero. but I dont know what to do with b.
     
  2. jcsd
  3. Sep 6, 2011 #2
    What you call F_x is not the force in the x direction but the magnitude of the force. You need to multiply F_x by a sin or cosine term to get the x component. But other then that it looks like you are on the right track.
     
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