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\[{{90}^{o}}\], 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                 \[\]