question_answer

An electric dipole of moment \[\vec{p}-=\left( -\hat{i}-3\hat{j}+2\hat{k} \right)\times {{10}^{-29}}\]C.m is at the origin (0, 0, 0). The electric field due to this dipole at \[\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}\](note that \[\vec{r}.\vec{p}=0\]) is paralled to                     [JEE MAIN Held on 09-01-2020 Morning]

A) \[\left( -\hat{i}-3\hat{j}+2\hat{k} \right)\] 

B) \[\left( +\hat{i}-3\hat{j}-2\hat{k} \right)\]

C) \[\left( -\hat{i}+3\hat{j}-2\hat{k} \right)\]

D) \[\left( +\hat{i}+3\hat{j}-2\hat{k} \right)\]

Correct Answer: D

Solution :

[d] \[\hat{E}=-\hat{p}\] \[\Rightarrow \hat{E}=-\left[ \frac{-\hat{i}-3\hat{j}+2\hat{k}}{\sqrt{14}} \right]\] \[\left| {\vec{E}} \right|=\frac{k\left| {\vec{p}} \right|}{{{r}^{3}}}\] \[\hat{E}\] is parallel to \[\left( \hat{i}+3\hat{j}-2\hat{k} \right)\]