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

The Correct Option is C

When a dipole $A B$ 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
$E =\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{2 p}{r^{3}}$
where $p$ is dipole moment. When dipole is rotated by $90^{\circ}$,
then electric field is given by
$E ' =\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{p}{r^{3}}$ ..(ii)
From Eqs. (i) and (ii), we get
$E =\frac{E}{2}$