Question

An electric dipole of moment $\overrightarrow{p}=(\hat{i}-3\hat{j}+2\hat{k})\times {10}^{-29}\text{Cm}$, is at the origin. The electric field due to this dipole at $\overrightarrow{r}=+\hat{i}+3\hat{j}+5\hat{k}$ (note that $\overrightarrow{r}\cdot \overrightarrow{p}=0)$ is parallel to:

• A. $(+\hat{i}-3\hat{j}-2\hat{k})$
• B. $(-\hat{i}+3\hat{j}-2\hat{k})$
• C. $(+\hat{i}+3\hat{j}-2\hat{k})$
• D. $(-\hat{i}-3\hat{j}+2\hat{k})$

Answer 1

The correct option is B $(-\hat{i}+3\hat{j}-2\hat{k})$

Since, $\overrightarrow{r}\cdot \overrightarrow{p}=0$

$\Rightarrow$ the given point lies on the equator of the dipole.

At an equatorial point, $\overrightarrow{E}$ is antiparallel to $\overrightarrow{p}$

$\Rightarrow$ a vector parallel to $\overrightarrow{E}$, will be antiparallel to $\overrightarrow{p}$

Now, $\overrightarrow{p}=(\hat{i}-3\hat{j}+2\hat{k})\times {10}^{-29}$

Considering all four options, the only vector that is antiparallel to $\overrightarrow{p}$, is $(-\hat{i}+3\hat{j}-2\hat{k})$

$\therefore \overrightarrow{E}$ is parallel to $(-\hat{i}+3\hat{j}-2\hat{k})$

Hence, $\left(B\right)$ is the correct answer.