question_answer

The ratio of electric fields on the axis and at equator of an electric dipole will be

A)  \[1:1\]       

B)  \[2:1\]

C)  \[4:1\]          

D)  \[1:4\]

Correct Answer: B

Solution :

The electric field on the axis of a dipole of length small compared to point where electric field is to be determined is \[{{E}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2p}{{{r}^{3}}}\] ?.(i) where p is electric dipole moment. Intensity at a point on the equatorial line of a dipole is \[{{E}_{E}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}N/C\] ??(ii) From Eqs. (i) and (ii), we get \[\frac{{{E}_{A}}}{{{E}_{E}}}=\frac{2p}{{{r}^{3}}}\times \frac{{{r}^{3}}}{p}=\frac{2}{1}\]