Field due to point charges - extremely strange error

[Ngineer]

Homework Statement

Find electric field anywhere on the x-axis due two two point charges
Q at (0,0,d)
-Q at (0,0,-d)

Homework Equations

The Attempt at a Solution

AttachedSomehow I am not getting the correct answer. I reviewed my steps with 4 people and we could not find the error!

I'm starting to think I've ruined the laws of physics.

 

[NascentOxygen]

Because you know one charge to be -Q then I would expect on the diagram you'd show its field line vector directed towards the charge.

 

[berkeman]

Homework Statement

Find electric field anywhere on the x-axis due two two point charges
Q at (0,0,d)
-Q at (0,0,-d)

Homework Equations

The Attempt at a Solution

AttachedSomehow I am not getting the correct answer. I reviewed my steps with 4 people and we could not find the error!

I'm starting to think I've ruined the laws of physics.

What is the z-component of E?

 

[Ngineer]

N.O. - The change in sign and direction was accounted for on the second line.
berkeman - the answer I got was -2q/4piEo * 1/(x2 + d2) az which is different from the "correct" answer by a factor of d/(x2 + d2)

 

[mfb]

It is hard to read that image.

You set up a vector and then write "=0." If that would be true, there would be nothing left to calculate.

Where do you calculate the z-component of your force?

 

[Ngineer]

Please discard that =0

I rewrote the solution for clarity

 

[Ngineer]

P/S. There a missing ² one line before the end but it should be obvious

 

[mfb]

I don't see what you did in the numerator between the first and second line. Your new numerator has both a different magnitude and direction.
You can make this way easier by combining the fractions and sorting the numerator by x and z components.