question_answer

Two short dipoles \[p\widehat{k}\,\,and\,\,\frac{p}{2}\widehat{k}\] are located at (0, 0, 0) and (1m, 0,2m) respectively. The resultant electric field due to the two dipoles at the point (1 m, 0, 0) is-

A) \[\frac{9p}{32\pi {{\in }_{0}}}\widehat{k}\]

B) \[\frac{-7p}{32\pi {{\in }_{0}}}\widehat{k}\]

C) \[\frac{-9p}{32\pi {{\in }_{0}}}\widehat{k}\]                  

D) \[\frac{4p}{32\pi {{\in }_{0}}}\widehat{k}\]

Correct Answer: B

Solution :

Due 1st dipole, electric field \[\overrightarrow{{{E}_{1}}}=\,\,\frac{1}{4\pi {{\in }_{0}}}\,\,\frac{p}{{{I}^{3}}}\,(-\widehat{k})\] Due to 2nd, dipole, electric field \[\overrightarrow{{{E}_{2}}}=\,\,\frac{1}{4\pi {{\in }_{0}}}\,\,\frac{2p/2}{{{2}^{3}}}\,\,\,(\widehat{k})\] \[{{\overrightarrow{E}}_{Net}}={{\overrightarrow{E}}_{1}}+{{\overrightarrow{E}}_{2}}\text{ }=\frac{1}{4\pi {{\in }_{0}}}\left( \frac{1}{8}-1 \right)\text{ }\widehat{k}\] \[=\frac{-7p}{32\pi {{\in }_{0}}}\,\,\widehat{k}\]