Three charges +2q,+3q,and -4q are situated at | vedclass

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(C) The dipole moment $\vec{p}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$.Given charges are $q_1 = +2q$ at $\vec{r}_1 = (0, -3

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

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(C) The dipole moment $\vec{p}$ of a system of charges is given by $\vec{p} = \sum q_i \vec{r}_i$.Given charges are $q_1 = +2q$ at $\vec{r}_1 = (0, -3a) = -3a\hat{j}$,$q_2 = +3q$ at $\vec{r}_2 = (2a, 0) = 2a\hat{i}$,and $q_3 = -4q$ at $\vec{r}_3 = (-2a, 0) = -2a\hat{i}$.Substituting these values into the formula:$\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} = (6qa + 8qa)\hat{i} - 6qa\hat{j}$$\vec{p} = 14qa\hat{i} - 6qa\hat{j}$$\vec{p} = 2qa(7\hat{i} - 3\hat{j})$

Column-$I$ (Angle between $\vec{p}$ and $\vec{E}$)	Column-$II$ (Potential energy of the dipole)
$a. 180^{\circ}$	$i. -pE$
$b. 120^{\circ}$	$ii. pE$
$c. 90^{\circ}$	$iii. \frac{1}{2} pE$
	$iv. 0$

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 the origin is . . . . . .

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