Electric field of a dipole at an offset point

[cj]

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1. Homework Statement

Homework Equations

I can't use voltage, nor polar coordinates (got to stick with cartesian).
Cartesian vector form of Coulomb's Law

The Attempt at a Solution

 

[haruspex]

[ Items related to the initial post's original format removed by moderator ] ...

However, your handwriting and images are fairly clear, and you have taken the trouble to number all of your equations, which helps enormously, so I will answer.

It asks for two specific cases, a point on the x-axis and a point on the y axis. You do not need to work with P in general position.
In your equations (3) and (5), compare the signs on the $\hat j$ terms.

 

[cj]

It asks for two specific cases, a point on the x-axis and a point on the y axis. You do not need to work with P in general position.
In your equations (3) and (5), compare the signs on the $\hat j$ terms.

Thank you. I appreciate your feedback. It, does, though, not help at all. What I provided is many steps beyond the scope of your suggestion, and focuses on how to handle the binomial version of the denominator, and how to process it. Again, thanks anyway.

 

[haruspex]

It, does, though, not help at all.

Then you have not paid proper attention to my final comment:

In your equations (3) and (5), compare the signs on the $\hat j$ terms.

[... some text unrelated to the problem at hand deleted by moderator]

 

[cj]

Then you have not paid proper attention to my final comment:
.

I did; I suspect you didn't read my post in its entirety - or you simply are stumped. I'd follow up with clarifying comments - but there's a ton in my post already.

 

[haruspex]

I did; I suspect you didn't read my post in its entirety - or you simply are stumped. I'd follow up with clarifying comments - but there's a ton in my post already.

Which post? Your original images or something since? I still don't see anywhere that you admit to having a sign wrong in equation 5.

 

[cj]

That was a typo: but it's the x-hat term in Eq. 5 (I prematurely assigned a "-" sign to reflect the -x direction of E_-; but didn't carry it through).

I disagree; the j-hat terms are indeed correct as written (this has been widely confirmed, and is a moot point).

 

[haruspex]

I disagree; the j-hat terms are indeed correct as written (this has been widely confirmed, and is a moot point).

Humour me: plug x=0 into equations 3 and 5, and consider y>>a. What do you notice?