Question

At a far away distance $r$ along the axis from an electric dipole, the electric field is $E$. Find the electric field at distance $2r$ along the perpendicular bisector.

• A. -$\frac{E}{4}$
• B. -$\frac{E}{16}$
• C. $\frac{E}{2}$
• D. $E$

Answer 1

The correct option is B -$\frac{E}{16}$

We know that electric field $E$, along the axis of dipole,

$E=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r^3}.....\left(1\right)$

where, $p$ is dipole moment.

The electric field in the direction of perpendicular bisector of dipole at a distance $2r$,

$E^{\prime }=\frac{1}{4\pi {ϵ}_0}\frac{p}{(2r{)}^3}.....\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$, we can see that
$E^{\prime }=\frac{E}{16}$

Moreover, $E^{\prime }$ is in the opposite direction of $p$ Hence,

$E^{\prime }=-\frac{E}{16}$

Hence, option (b) is correct answer.