Question

The electric field due to an electric dipole at a distance $r$ from its centre in axial position is $E$. If the dipole is rotated through an angle of $90^{\circ }$ about its perpendicular axis, the electric field at the same point will be

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

Answer 1

Answer: (C)

When a dipole $AB$ of very small length is taken, then for a point $P$ located at a distance $r$ from the axis the electric field is given by
$E=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{2p}{r^3}$
where $p$ is dipole moment. When dipole is rotated by $90^{\circ }$,
then electric field is given by
$E^{\prime }=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{p}{r^3}$ ..(ii)
From Eqs. (i) and (ii), we get
$E=\frac{E}{2}$