question_answer

Let eqbe the electric field due to a dipole in its  axial plane distan\[l\] and let \[{{\text{E}}_{q}}\]be the field  in the equatorial plane distant \[l,\]then the relation between \[{{E}_{a}}\]and \[{{E}_{q}}\]will be

A) \[{{E}_{a}}=4{{E}_{q}}\]

B)  \[{{E}_{q}}=2{{E}_{a}}\]

C)  \[{{E}_{a}}=2{{E}_{q}}\]

D) \[{{E}_{q}}=3{{E}_{a}}\]

Correct Answer: C

Solution :

 Intensity of electric field at a point on the axis of dipole is given by \[{{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{o}}}.\frac{2p}{{{r}^{3}}}N/C\]     ?(i) where, p is dipole moment. Intensity of electric field at a point on the equatorial line of dipole is given by \[{{E}_{q}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}N/C\] ?(ii) Dividing Eq. (i).by Eq. (ii), we get \[\frac{{{E}_{a}}}{{{E}_{q}}}=\frac{2}{1}\Rightarrow {{E}_{a}}=2{{E}_{q}}\]