question_answer

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 \[{{90}^{o}}\]about its perpendicular axis, the electric field at the same point will be

A)  \[E\]              

B)  \[\frac{E}{4}\]

C)  \[\frac{E}{2}\]            

D)  \[2E\]

Correct Answer: C

Solution :

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 \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2p}{{{r}^{3}}}\] ??(i) where p is dipole moment. When dipole is rotated by \[{{90}^{o}},\] then electric field is  given by \[E'=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}\] ?.(ii) From Eqs. (i) and (ii), we get \[E'=\frac{E}{2}\]