# Derive equation for electric potential of electric dipole

I'm not understanding how the equation of the electric field due to an electric dipole is derived. This is how my book derives it:

Say you have electric dipole composed of charges +q and -q a distance d apart, with the negative charge at the origin of the z-axis. Then, at any point z, the E field is:

$\frac{kq}{(z-\frac{1}{2}d)^{2}}$ - $\frac{kq}{(z+\frac{1}{2}d)^{2}}$

Below is the exact picture of the situation from my book:

But shouldn't the equation be:
$\frac{kq}{(z-d)^{2}}$ - $\frac{kq}{z^{2}}$

??

In my book's equation, it looks like they're just treating the two charges as if they're at the same point (the midpoint, corresponding to (1/2)d)....I know that for large z, this wouldn't matter much, but still, what if you want small z...

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## Answers and Replies

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You have misunderstood the position of the origin. z=0 is between the charges (the dot).

You have misunderstood the position of the origin. z=0 is between the charges (the dot).
Oh! wow im stupid thanks lol