Write the equation for the electric field produced by an electric dipole at a point on its axial line,given the condition $r >> a$.
(N/A) The electric field $E$ at a point on the axis of an electric dipole at a distance $r$ from the center is given by the formula:
$E = \frac{1}{4\pi\epsilon_0} \frac{2pr}{(r^2 - a^2)^2}$
where $p$ is the dipole moment and $2a$ is the distance between the charges.
For the condition $r >> a$,we can neglect $a^2$ in comparison to $r^2$ in the denominator.
Thus,the equation simplifies to:
$E = \frac{1}{4\pi\epsilon_0} \frac{2pr}{r^4}$
$E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$
$E = \frac{1}{4\pi\epsilon_0} \frac{2pr}{(r^2 - a^2)^2}$
where $p$ is the dipole moment and $2a$ is the distance between the charges.
For the condition $r >> a$,we can neglect $a^2$ in comparison to $r^2$ in the denominator.
Thus,the equation simplifies to:
$E = \frac{1}{4\pi\epsilon_0} \frac{2pr}{r^4}$
$E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$
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