Determing location where electric field is zero?

[Ascendant78]

Homework Statement

Homework Equations

See #1

The Attempt at a Solution

Based on the information in the question, I did what I could, but in the back of the book they have an answer of -9.9a and I have no idea how?

For the +3q on the right, I set the denominator to (2a+r)^2, since its distance would be the square of both the 2a between them as well as the additional r distance between the point and -2q. I am thinking they somehow managed to relate a to r to get rid of r, but I can't seem to figure out how I can do that or in some other way get rid of r?

 

[maajdl]

Why (r+2a) and not (r-2a) ?
Where is the b charge located in your system of coordinates? At x=2a or at x=-2a?
Why did you expand (r+2a)², does that make your calculations simpler?

 

[grzz]

All is correct except that (r^{2} + 4ar + 4a^{2}) is suddenly changed to
(r^{2} + 4a^{2}).

 

[Ascendant78]

All is correct except that (r^{2} + 4a + 4a^{2}) is suddenly changed to
(r^{2} + 4a^{2}).

Thanks, but I'm not seeing how you are getting that? Wouldn't I want to square their combined sum?

 

[grzz]

I meant that the term '4ar' must be kept and not lost on the way.

 

[Ascendant78]

I meant that the term '4ar' must be kept and not lost on the way.

Oh, yes I did correct that on my personal scribble, just not on that page. Even after I did that however, I still end up with r values in the equation that I can't seem to get rid of as shown here:

 

[Ascendant78]

This thing is due tomorrow and I haven't heard back from the professor either, so if anyone has any suggestions, I'm all ears? I did change up my signs, realizing the direction should be expressed as the point from the source of the charge TO the point I am trying to locate, rather than the reverse which I started with. It's frustrating because our book didn't explain how to approach a problem like this, but our professor threw it at us.