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 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                 \[E=\frac{E}{2}\]