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

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tsuwal
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Homework Statement



https://www.physicsforums.com/attachments/56019



Homework Equations





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?
 


Sorry, here it is:

Handwritten diagram on x-y axes: charge q1 at (-d, 0) and charge q2 at (d, 0), a point at (0, h) with forces F1 and F2 drawn as arrows, and the text 'Find h such that F1e(0,h) + F2e(0,h) = MAX, q1 = q2'.
 


I do not think the final equation is correct. Show how you differentiated the previous equation.
 


[itex]\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}´*sin(\alpha)+cos(\alpha)^{2}*sin(\alpha)´=0 \Leftrightarrow <br /> -2*sin(\alpha)*cos(\alpha)+cos(\alpha)^{3}=0 \Leftrightarrow cos(\alpha)^{2}=2*Sin(\alpha)[/itex]
 


tsuwal said:
[itex]\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}´*sin(\alpha)+cos(\alpha)^{2}*sin(\alpha)´=0 \Leftrightarrow <br /> -2*sin(\alpha)*cos(\alpha)+cos(\alpha)^{3}[/itex]

This should be ## -2*sin(\alpha)*cos(\alpha)*sin(\alpha)+cos(\alpha)^{3} ##