Write the equation for the electric field produced by an electric dipole at a point on its equatorial line,given the condition $r >> a$ (where $r$ is the distance from the center and $2a$ is the dipole length).

(N/A) The electric field $E$ at a point on the equatorial line of an electric dipole of dipole moment $p$ at a distance $r$ from the center is given by the formula:
$E = \frac{1}{4\pi\epsilon_0} \frac{p}{(r^2 + a^2)^{3/2}}$
For the condition $r >> a$,we can neglect $a^2$ in comparison to $r^2$ in the denominator.
Thus,$(r^2 + a^2)^{3/2} \approx (r^2)^{3/2} = r^3$.
The equation simplifies to:
$E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$
The direction of this electric field is opposite to the direction of the dipole moment vector $p$.