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

(a) $\displaystyle (\hat{i} – 3 \hat{j}-2\hat{k})$

(b) $\displaystyle (-\hat{i} – 3 \hat{j} + 2\hat{k})$

(c) $\displaystyle (\hat{i} + 3 \hat{j}-2\hat{k})$

(d) $\displaystyle (- \hat{i} + 3 \hat{j}- 2\hat{k})$

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Sol: $\displaystyle \vec{p} = (-\hat{i}-3\hat{j} + 2\hat{k}) \times 10^{-29} C m $

$\displaystyle \vec{r} = \hat{i} + 3 \hat{j} + 5 \hat{k}$

As , $\displaystyle \vec{r}.\vec{p} = 0$ , It means $\vec{r}$ is perpendicular to $\vec{p}$ Therefore point lies on equilateral plane . Thus electric field is anti-parallel to dipole moment or $\vec{E}|| (-\vec{p})$

$\displaystyle \vec{E}|| (-(-\hat{i}-3\hat{j} + 2\hat{k}))$

$\displaystyle \vec{E}|| (\hat{i} + 3\hat{j} – 2\hat{k}) $