Q57 / 75 · JEE Main 2026 (24 January Shift 1) · Physics
Three charges $+2 q,+3 q$ and $-4 q$ are situated at $(0,-3 a),(2 a, 0)$ and $(-2 a, 0)$ respectively in the $x y$ plane. The resultant dipole moment about origin is $\_\_\_\_$.
- Correct answerA$2 q a(7 \hat{i}-3 \hat{j})$
- B$2 q a(3 \hat{j}-\hat{i})$
- C$2 q a(3 \hat{i}-7 \hat{j})$
- D$2 q a(3 \hat{j}-7 \hat{i})$
Solution
The dipole moment is given by:
$\vec{p} = q_1\vec{r}_1 + q_2\vec{r}_2 + q_3\vec{r}_3$
$\vec{p} = (2q)(-3a)\hat{j} + (3q)(2a)\hat{i} + (-4q)(-2a)\hat{i}$
$\vec{p} = -6qa\hat{j} + 6qa\hat{i} + 8qa\hat{i}$
$\vec{p} = 14qa\hat{i} - 6qa\hat{j}$
$\vec{p} = 2qa(7\hat{i} - 3\hat{j})$
$\vec{p} = q_1\vec{r}_1 + q_2\vec{r}_2 + q_3\vec{r}_3$
$\vec{p} = (2q)(-3a)\hat{j} + (3q)(2a)\hat{i} + (-4q)(-2a)\hat{i}$
$\vec{p} = -6qa\hat{j} + 6qa\hat{i} + 8qa\hat{i}$
$\vec{p} = 14qa\hat{i} - 6qa\hat{j}$
$\vec{p} = 2qa(7\hat{i} - 3\hat{j})$
Hence, the correct answer is option: 'A'.