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

1. Feb 23, 2013

### tsuwal

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:

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

Taking the rerivative to find the maximum we get:

$\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}=2*Sin(\alpha)$

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. Feb 23, 2013

### voko

Re: Find the point where the eletrostatic force is maximum. (With draw

The attachment is broken.

3. Feb 23, 2013

### tsuwal

Re: Find the point where the eletrostatic force is maximum. (With draw

Sorry, here it is:

4. Feb 23, 2013

### voko

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.

5. Feb 23, 2013

### tsuwal

Re: Find the point where the eletrostatic force is maximum. (With draw

$\frac{d cos(\alpha)^{2}*Sin(\alpha)}{d\alpha}=0 \Leftrightarrow cos(\alpha)^{2}´*sin(\alpha)+cos(\alpha)^{2}*sin(\alpha)´=0 \Leftrightarrow -2*sin(\alpha)*cos(\alpha)+cos(\alpha)^{3}=0 \Leftrightarrow cos(\alpha)^{2}=2*Sin(\alpha)$

6. Feb 23, 2013

### voko

Re: Find the point where the eletrostatic force is maximum. (With draw

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

7. Feb 23, 2013

### tsuwal

Re: Find the point where the eletrostatic force is maximum. (With draw

Thanks, don't know how I missed that!

8. Feb 23, 2013

### voko

Re: Find the point where the eletrostatic force is maximum. (With draw

I assume you can continue from here.