JEE PYQ: Electrostatics Question 35
Question 35 - 2020 (09 Jan Shift 1)
An electric dipole of moment $\vec{p} = (\hat{i} - 3\hat{j} + 2\hat{k}) \times 10^{-29}$ C.m is at the origin (0, 0, 0). The electric field due to this dipole at $\vec{r} = +\hat{i} + 3\hat{j} + 5\hat{k}$ (note that $\vec{r} \cdot \vec{p} = 0$) is parallel to:
(1) $(+\hat{i} - 3\hat{j} - 2\hat{k})$
(2) $(-\hat{i} + 3\hat{j} - 2\hat{k})$
(3) $(+\hat{i} + 3\hat{j} - 2\hat{k})$
(4) $(-\hat{i} - 3\hat{j} + 2\hat{k})$
Show Answer
Answer: (3)
Solution
Since $\vec{r} \cdot \vec{p} = 0$, this is the equatorial plane. In the equatorial plane, $\vec{E}$ is antiparallel to $\vec{p}$. So $\vec{E} \parallel -\vec{p} = (-\hat{i} + 3\hat{j} - 2\hat{k})$… But $\vec{E}$ must be antiparallel to the dipole moment direction: $\vec{E} \parallel (+\hat{i} + 3\hat{j} - 2\hat{k})$. Answer is (3).
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