Three charges , and are situated at , and respectively in the plane. The resultant dipole moment about origin is _____. [2026]

Question

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 _____. [2026]

Smart Achievers · Accepted Answer

(2)

$\vec{p} = q_{1} {\vec{r}}_{1} + q_{2} {\vec{r}}_{2} + q_{3} {\vec{r}}_{3}$

$\vec{p} = (2 q) (- 3 a) \hat{j} + (3 q) (2 a) \hat{i} + (- 4 q) (- 2 a) \hat{i}$

$\vec{p} = 2 q a (7 \hat{i} - 3 \hat{j})$

Solution

Q.
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 _____. [2026]

1 $2 q a (3 \hat{j} - 7 \hat{i})$

2 $2 q a (7 \hat{i} - 3 \hat{j})$

3 $2 q a (3 \hat{i} - 7 \hat{j})$

4 $2 q a (3 \hat{j} - \hat{i})$

Ans.
(2)

$\vec{p} = q_{1} {\vec{r}}_{1} + q_{2} {\vec{r}}_{2} + q_{3} {\vec{r}}_{3}$

$\vec{p} = (2 q) (- 3 a) \hat{j} + (3 q) (2 a) \hat{i} + (- 4 q) (- 2 a) \hat{i}$

$\vec{p} = 2 q a (7 \hat{i} - 3 \hat{j})$

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Solution

Q. Three charges +2q, +3q and -4q are situated at (0,-3a), (2a,0) and (-2a,0) respectively in the xy plane. The resultant dipole moment about origin is _____. [2026]

1 2qa(3j^-7i^)

2 2qa(7i^-3j^)

3 2qa(3i^-7j^)

4 2qa(3j^-i^)

Ans. (2) p→=q1r→1+q2r→2+q3r→3 p→=(2q)(-3a)j^+(3q)(2a)i^+(-4q)(-2a)i^ p→=2qa(7i^-3j^)