Question

4 charges are placed each at a distance 'a' from an origin. The dipole moment of
configuration is:

• A. $2qa\hat{j}$
• B. $3qa\hat{j}$
• C. $2qa[\hat{i}+\hat{j}]$
• D. none

Answer 1

The correct option is A $2qa\hat{j}$

Charge at A and c point can be a combination of (2q+q) and ((-q)+(-q)) respectively.

2q charge make a dipole with -2q charge present at B point has dipole moment is $P_2$ and another q charge at the point A make a dipole with -q charge present at C point has dipole moment is $P_2$ another -q charge present at the D point has dipole moment is $P_3$ make dipole with q charge present at d position

$\overrightarrow{P_1}=2qa\hat{i}+2qa\hat{j}$

$\overrightarrow{P_2}=-qa\hat{i}+qa\hat{j}$

$\overrightarrow{P_3}=-qa\hat{i}-qa\hat{j}$

resultant dipole moment is &&\vec{P}$

$\Rightarrow \overrightarrow{P}=\overrightarrow{P_1}+\overrightarrow{P_2}+\overrightarrow{P_3}$

$\Rightarrow \overrightarrow{P}=(2qa\hat{i}+2qa\hat{j})+(-qa\hat{i}+qa\hat{j})+(-qa\hat{i}-2q\hat{j})$

$\Rightarrow \overrightarrow{P}=2qa\hat{j}.$

Hence the A option is correct.