Question

The electric field due to an electric dipole at a distance $r$ from its center in axial position is $E.$ If the dipole is rotated through an angle of ${90}^o$ 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)

$\frac{E}{2}$

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