question_answer

Let \[{{E}_{a}}\] be the electric field due to a dipole in its axial plane distant \[l\] and let \[{{E}_{q}}\] 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                 \[{{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2p}{{{r}^{3}}}N/C\]                        ? (i) where, \[p\] is dipole moment. Intensity of electric field at a point on the equatorial line of dipole is given by                      \[{{E}_{q}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{p}{{{r}^{3}}}N/C\]                          ... (ii) Dividing Eq. (i) by Eq. (ii), we get                 \[\frac{{{E}_{a}}}{{{E}_{q}}}=\frac{2}{1}\Rightarrow {{E}_{a}}=2{{E}_{q}}\]