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Find the point where the eletrostatic force is maximum. (With drawing)

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data

    View attachment 56019



    2. Relevant equations



    3. The attempt at a solution

    The net force will be:

    [itex]F=\frac{2*Sin(\alpha)*q1*q}{(d/cos(\alpha))^{2}}=cos(\alpha)^{2}*Sin(\alpha)*qq1/d^{2}[/itex]

    Taking the rerivative to find the maximum we get:

    [itex]\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}=2*Sin(\alpha)[/itex]

    How do I solve this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 23, 2013 #2
    Re: Find the point where the eletrostatic force is maximum. (With draw

    The attachment is broken.
     
  4. Feb 23, 2013 #3
    Re: Find the point where the eletrostatic force is maximum. (With draw

    Sorry, here it is:

    pf.png
     
  5. Feb 23, 2013 #4
    Re: Find the point where the eletrostatic force is maximum. (With draw

    I do not think the final equation is correct. Show how you differentiated the previous equation.
     
  6. Feb 23, 2013 #5
    Re: Find the point where the eletrostatic force is maximum. (With draw

    [itex]\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}´*sin(\alpha)+cos(\alpha)^{2}*sin(\alpha)´=0 \Leftrightarrow
    -2*sin(\alpha)*cos(\alpha)+cos(\alpha)^{3}=0 \Leftrightarrow cos(\alpha)^{2}=2*Sin(\alpha) [/itex]
     
  7. Feb 23, 2013 #6
    Re: Find the point where the eletrostatic force is maximum. (With draw

    This should be ## -2*sin(\alpha)*cos(\alpha)*sin(\alpha)+cos(\alpha)^{3} ##
     
  8. Feb 23, 2013 #7
    Re: Find the point where the eletrostatic force is maximum. (With draw

    Thanks, don't know how I missed that!
     
  9. Feb 23, 2013 #8
    Re: Find the point where the eletrostatic force is maximum. (With draw

    I assume you can continue from here.
     
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