Electric Field along the x axis of a dipole

[Libohove90]

Homework Statement

Show that the field on the x-axis for the dipole (negative on the right, positive on the left separated by 2a) is given by the equation E = kq / x^3 for x >>a.

Homework Equations

Coulomb's Law F = kq1q2 / r^2
E = F/q = kQ / r^2

The Attempt at a Solution

Since its a vector sum, I just add the two equations to get E = kq / r^2 + k(-q) / r^2

The solutions manual gives me E = kq / (x-a)^2 + k(-q) / (x+a)^2

I feel stupid but I seem to be hitting a wall. Why does the positive charge have (x-a)^2, while the negative charge has a (x+a)^2? What does 'a' represent? I keep confusing myself, can someone clarify this for me? I understand everything except the nature of the denominators. Thanks

 

[tiny-tim]

Hi Libohove90!

(try using the X² and X₂ icons just above the Reply box )

Why does the positive charge have (x-a)^2, while the negative charge has a (x+a)^2? What does 'a' represent?

If you're at position x, you're x-a from the nearer charge, and x+a from the further charge.