Electric Field at a Distant Point

[davezhan]

1. Consider the electric dipole on the x-axis where a positive charge q is at (a,0) and a negative charge -q is at (-a,0) such that the distance between the two charges is 2a. Show that the electric field at a distant point on the +x axis is
E(x)= 4kqa/x^3.



2. Homework Equations : E=kq1q2/r^2



3. The Attempt at a Solution :

E=kq/x^2 - kq/(x+2a)^2

E(simplified)=kq[x^-2 - (x^2+4a)^-1]

E=4kqa/(x^4+4x^2a)

This clearly gives me the wrong solution, but I know it works when I switch my r values.

Why is it that I have to use x-a and x+a for r instead of x and x-2a?

Why does shifting the y-axis change the answer since x>>2a, it shouldn't matter, but I'm getting a different solution using this approach.

Please help me understand this problem! Thanks!

 

[rl.bhat]

E(simplified)=kq[x^-2 - (x^2+4a)^-1]

E=4kqa/(x^4+4x^2a)
Check this simplification.
E = kq[1/x^2 - 1/(x + 2a)^2]
= kq[(x+2a)^2 - x^2]/(x)^2*(x+2a)^2
= kq[4ax+4a^2]/(x)^2*(x+2a)^2
= kq*4ax*(1+a/x)/(x)^4(1+2a/x)^2
Neglect a/x term and find E.

 

[vela]

E=kq/x^2 - kq/(x+2a)^2

E(simplified)=kq[x^-2 - (x^2+4a)^-1]

The second line is obviously wrong because you can't add $x^2$ to $4a$. They have different units. It's not clear to me what you were trying to do.