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) When dipole is rotated by \[\text{9}{{\text{0}}^{\text{o}}}\text{,}\]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 \[\]