Where Is the Electric Field Zero Between Two Charged Particles?

[electricman]

Homework Statement

Two particles with positive charges q1 and q2 are separated by a distance s.

Along the line connecting the two charges, at what distance from the charge q1 is the total electric field from the two charges zero?

Homework Equations

Express your answer in terms of some or all of the variables s , q1 , q2 and k=1/(4pi epsilon)

The Attempt at a Solution

I got s=sqrt(q1(d-s)^2 / q2), but i think its wrong.

Anyone who knows?

 

[altegron]

You should probably wait for someone more knowledgeable on this subject to post an answer, but here is what I came up with:

It looks like you solved for s instead of the distance from q1 where the field is 0.

If your problem looks like this:

            |----------s----------|
-----------(q1)-----0------------(q2)---------
            |---x---|-----s-x-----|

I figured that the magnitude of E from each (+) charge would be equal so I made the equation:

<br /> {k}_{e}\frac{{q}_{1}}{x^2} = {k}_{e}\frac{{q}_{2}}{(s-x)^2}<br />

Divide both sides by ke:

<br /> \frac{{q}_{1}}{x^2} = \frac{{q}_{2}}{(s-x)^2}<br />

Cross multiply, then divide by x^2:

<br /> \frac{(s-x)^2}{x^2} = \frac{{q}_{2}}{q}_{1}<br />

Square root both sides, then distribute the x denominator:

<br /> \frac{s}{x} - \frac{x}{x} = \sqrt\frac{{q}_{2}}{q}_{1}<br />

Simplify x/x to 1 and add to other side then multiply by x:

<br /> s = (\sqrt{\frac{{q}_{2}}{q}_{1}} + 1)x<br />

Finally divide to get x alone:

<br /> x = \frac{s}{\sqrt{\frac{{q}_{2}}{q}_{1}} + 1}<br />

So that's my final answer, which I'm pretty sure is correct but then I usually make some careless error. (Sorry if I showed too many baby steps with the algebra there.)

Anyways, hope that helps.

 

[electricman]

yes, i got the same so i guess that its correct.

Thanks for the help